# what does a large iqr mean

Quartiles divide a rank-ordered data set into four equal parts. The small number of people with higher incomes also increase the standard deviation, so a small number of high incomes gives the misleading impression that typical incomes in the … range is Q3 minus Q1, so IQR = 6.5 - 3.5 = 3. A small interquartile range means that the data are very consistent (most values lie close to each other). Data & Statistics. To compute an interquartile range using this definition, first remove observations from the lower quartile. If the same data is divided into 100 parts, each part is called a percentile. The quartiles can be determined in the same way we determined the median, except we consider each half of the data set separately. Frequently, side-by-side boxplots are drawn vertically. If the histogram is close to symmetric, then the mean and median are close to each other. . If IQR is large, data are more spread out from the median, otherwise they are closer. Interquartile range example. The mean, median, mode, range, and IQR are all doubled when we double the values in the data set. There are several methods for determining outliers in a sample. Organizing the Data Set Gather your data. In some texts, the interquartile range Data & Statistics. Multiply the interquartile range (IQR) by 1.5 (a constant used to discern outliers). Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average. The interquartile range is a measure of the "central tendency" just like the standard deviation. It is frequently calculated as a means of identifying what the range of an average performance should be. 0.5 C. 0 D. Unknown What statistics are needed to draw a box plot? Interquartile range (IQR) = Q3 - Q1 = 85 - 41 = 44. divide each part are called the first, second, and third quartiles; The interquartile range is a measure of variability based on splitting data into quartiles. Sort by: Top Voted. 4 th calculation: Interquartile Range = UQ – LQ = 19 – 8. is defined differently. Chapter 1: Vocabulary - … Out of 6,028,151 records in the U.S. Social Security Administration public data, the first name Iqr was not present. No matter what value we multiply by the data set, the mean, median, mode, range, and IQR will all be multiplied by the same value. Figure 10 - Interquartile Range with Odd Sample Size. When a data set has outliers or extreme values, we summarize a typical value using the median as opposed to the mean. The interquartile range (IQR) is the range from the 25 th percentile to the 75 th percentile, or middle 50 percent, of a set of numbers. The interquartile range is a measure of the "central tendency" just like the standard deviation. Are there outliers in any of the variables? What does IQR mean? Negative IQR is fine, if your data is in descending order. Quartile: A quartile is a statistical term describing a division of observations into four defined intervals based upon the values of the data and how … To find the interquartile range of your 8 data points, you first find the values at Q1 and Q3.. Note: If you sort data in descending order, IQR will be -44. It can be calculated using three simple formulas. The interquartile range (IQR) is a measure of variability, It is frequently calculated as a means of identifying what the range of an average performance should be. Median, Quartiles and Percentiles for Ungrouped Data or Discrete Data, Find the median, lower quartile, upper quartile, interquartile range and range of the given discrete data, with video lessons, examples and step-by-step solutions. The interquartile range IQR is defined as: = − That is, it is calculated as the range of the middle half of the scores. Please look for them carefully. The IQR is the difference between Q3 and Q1. Date last modified: May 17, 2016. What Does Interquartile Range Mean? The magnitude will be same, just sign will differ. Click below the question to view the answer. The interquartile range (IQR) is the range from the 25 th percentile to the 75 th percentile, or middle 50 percent, of a set of numbers. This site contains various terms related to bank, Insurance companies, Automobiles, Finance, Mobile phones, software, computers,Travelling, … Which statistics are most appropriate to summarize the average or typical value and the dispersion? The Interquartile Range (IQR) . Statistics CH 3. 0.5 C. 0 D. Unknown What statistics are needed to draw a box plot? If the histogram is skewed right, the mean is greater than the median. The interquartile range (IQR) is the difference between the first quartile and third quartile. Interquartile range (IQR) is a measure of how the middle [math]50\%[/math] of data are spread around the median. and other Percentiles. It just we negate smaller values from larger values, we prefer ascending order (Q3 - … By Deborah J. Rumsey . Multiply the number of values in the data set (8) by 0.25 for the 25th percentile (Q1) and by 0.75 for the 75th percentile (Q3). An Alternative Definition for IQR In some texts, the interquartile range is defined differently. With this example, one can say that the middle 50% of the salaries spans \\$16,250 (or spans from \\$33,250 to \\$49,500). The IQR is the length of the box on a boxplot. How unique is the name Iqr? For clarity, we have so far used a very small subset of the Framingham Offspring Cohort to illustrate calculations of summary statistics and determination of outliers. The interquartile range is more useful as a measure of spread than the range because of this stability. Notice that only a few numbers are needed to determine the IQR and those numbers are not the extreme observations that may be outliers. Next lesson. compute the difference between the largest and smallest values. The interquartile range is defined as follows: For the sample (n=10) the median diastolic blood pressure is 71 (50% of the values are above 71, and 50% are below). Chapter 1: Vocabulary - … A. Top IQR abbreviation related to Quality: Inpatient Quality Reporting Quality IQR abbreviation meaning defined here. The mean is too high to represent the large number of people making less than \$20,000 a year. AP Statistics Tutorial: Measures of Variability. When there are outliers in a sample, the median and interquartile range are used to summarize a typical value and the variability in the sample, respectively. Quality IQR abbreviation meaning defined here. Note: If you sort data in descending order, IQR will be -44. A very popular method is based on the following: Outliers are values below Q1-1.5(Q3-Q1) or above Q3+1.5(Q3-Q1) or equivalently, values below Q1-1.5 IQR or above Q3+1.5 IQR. And this will always be true. When a data set has outliers, variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles. What does a small IQR mean? The best summary of a typical diastolic blood pressure is the mean (in this case 71.3) and the best summary of variability is given by the standard deviation (s=7.2). middle values; that is, Q3 = (6 + 7)/2 or Q3 = 6.5. For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. . IQR = 11. The lower 50% of the observations B. The interquartile range is the middle half of the data. The values that split each part are known as the first, second and third quartile. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean, on average. With this example, one can say that the middle 50% of the salaries spans \\$16,250 (or spans from \\$33,250 to \\$49,500). The interquartile range (IQR) would If the histogram is skewed right, the mean is greater than the median. of the data set. Negative IQR is fine, if your data is in descending order. most of the data is close to the median. What does IQR stand for in Quality? The IQR describes the middle 50% of values when ordered from lowest to highest. What does this IQR represent? The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range.The IQM is very similar to the scoring method used in sports that are evaluated by a panel of judges: discard the lowest and the highest scores; calculate the mean value of the remaining scores Subtract 1.5 x (IQR) from the first quartile. Fun Facts about the name Iqr. It is usually used in conjunction with a measure of central tendency, such as the mean or median, to provide an overall description of a set of data. Add 1.5 x (IQR) to the third quartile. the largest and smallest values in the middle 50% of a set of When the sample size is 9, the median is the middle number 72. even number of data points in the first half of the data set, the middle value Any number greater than this is a suspected outlier. Standard deviation can be difficult to interpret as a single number on its own. 55 terms. Machine learning algorithms are very sensitive to the range and distribution of data points. There are 5 values below the median (lower half), the middle value is 64 which is the first quartile. The formula for this is: IQR = Q 3 - Q 1 There are many measurements of the variability of a set of data. Find IQR using the formula IQR = Quartile 3 – Quartile 1. The median and quartiles are indicated below. Interpretation: There are 11cm between the size of pebbles at the quarter, and three-quarters dispersion around the median pebble size on this beach. It is defined as the difference between the largest and smallest values in the middle 50% of a set of data. YOU MIGHT ALSO LIKE... 23 terms. . Now that you understand quartiles and interquartile range, there are other ways to interpret these concepts. No matter what value we multiply by the data set, the mean, median, mode, range, and IQR will all be multiplied by the same value. The RPD for my data is 1.85 while RPIQ is 3.22 which means that the interquartile range (IQR) is larger than the standard deviation (std) for the same distribution. One of the most important steps in data pre-processing is outlier detection and treatment. The interquartile range is the third quartile (Q3) minus the first quartile (Q1). Any number less than this is … If IQR is large, data are more spread out from the median, otherwise they are closer. Now that you understand quartiles and interquartile range, there are other ways to interpret these concepts. The quartiles are determined in the same way looking at the lower and upper halves, respectively. from the upper quartile. Quartile: A quartile is a statistical term describing a division of observations into four defined intervals based upon the values of the data and how … Calculate the interquartile range for the data. It is possible the name you are searching has less than five occurrences per year. The z-score and t-score (aka z-value and t-value) show how many standard deviations away from the mean of the distribution you are, assuming your data follow a z-distribution or a t-distribution.. Half the data points lie within the interquartile range (and that's true whether you have 20 measurements or 10,000). If the same data is divided into 100 parts, each part is called a percentile. If you're learning this for a class and taking a test, you … The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range.The IQM is very similar to the scoring method used in sports that are evaluated by a panel of judges: discard the lowest and the highest scores; calculate the mean value of the remaining scores The interquartile range is the middle half of the data. Up Next. and other Percentiles. When there are no outliers in a sample, the mean and standard deviation are used to summarize a typical value and the variability in the sample, respectively. Possible IQR meaning as an acronym, abbreviation, shorthand or slang term vary from category to category. Modeling Data. The interquartile range is 77 – 64 = 13; the interquartile range is the range of the middle 50% of the data. is the average of the two middle values; that is, The RPD for my data is 1.85 while RPIQ is 3.22 which means that the interquartile range (IQR) is larger than the standard deviation (std) for the same distribution. Statistics CH 3. Interquartile range (IQR) is a measure of how the middle [math]50\%[/math] of data are spread around the median. Calculate the interquartile range for the data. Since there are an 1 B. To compute an interquartile range using this definition, first remove Organizing the Data Set Gather your data. The same approach is used in the upper half to determine the third quartile ((77+81)/2=79). Variance and standard deviation of a population. . Again, since the second half of the data set has an even The IQR is the length of the box on a boxplot. quartiles. Machine learning algorithms are very sensitive to the range and distribution of data points. An outlier is any value that lies more than one and a half times the length of the box from either end of the box. What does a small IQR mean? It just we negate smaller values from larger values, we prefer ascending order (Q3 - … What does the interquartile range describe? Interquartile range example. and they are denoted by Q1, Q2, and Q3, respectively. Find IQR using the formula IQR = Quartile 3 – Quartile 1. 4 th calculation: Interquartile Range = UQ – LQ = 19 – 8. Add 1.5 x (IQR) to the third quartile. The Interquartile Range (IQR) . Table 14 - Limits for Assessing Outliers in Characteristics Measured in the n=10 Participants. For your interest, Table 15 displays the means, standard deviations, medians, quartiles and interquartile ranges for each of the continuous variable displayed in Table 13 in the full sample (n=3,539) of participants who attended the seventh examination of the Framingham Offspring Study. Interpretation: There are 11cm between the size of pebbles at the quarter, and three-quarters dispersion around the median pebble size on this beach. Interquartile range review. Any number greater than this is a suspected outlier. A. The interquartile range is the third quartile (Q3) minus the first quartile (Q1). A measure of spread, sometimes also called a measure of dispersion, is used to describe the variability in a sample or population. Figure 9 - Interquartile Range with Even Sample Size. If the histogram is close to symmetric, then the mean and median are close to each other. And this will always be true. Based solely on a comparison of the means and medians in Table 15 above, there is evidence that there was one or more characteristics with values that were outliers? Table 15 - Summary Statistics on Sample of (n=3,539) Participants. The middle 50% of the observations C. The upper 50% of the observations D. The lower 25% and the upper 25% of the observations When applying the special rule of addition for mutually exclusive events, the joint probability is: A. One of the most important steps in data pre-processing is outlier detection and treatment. The lower 50% of the observations B. What does IQR stand for in Quality? most of the data is close to the median. Box plots are useful as they show outliers within a data set. Standard deviation can be difficult to interpret as a single number on its own. we are left with: 4, 5, 5, 6. There are 4 values in the lower half, the first quartile is the mean of the 2 middle values in the lower half ((64+64)/2=64). The middle blue line is median and the blue lines that enclose the blue region are Q1-1.5*IQR and Q3+1.5*IQR.Unlike mean and std, the blue region created by median and IQR … Purplemath. Table 16 displays the observed minimum and maximum values along with the limits to determine outliers using the quartile rule for each of the variables in the full sample (n=3,539). Then, from the remaining observations, Quartile divides the range of data into four equal parts. https://www.khanacademy.org/.../cc-6th/v/calculating-interquartile-range-iqr Q3−Q1). The interquartile range is a stable measure of spread in that it is not influenced by unusually large or unusually small values. observations from the lower quartile. Interquartile range (IQR) Interquartile range review. shows that the numbers are spread out. Q1 = (3 + 4)/2 or Q1 = 3.5. Modeling Data. Weird things about the name Iqr: The name spelled backwards is Rqi. It is defined as the difference between For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. This is the case because skewed-right data have a few large values that drive the mean upward but do not affect where the exact middle of the data is (that is, the median). Interquartile range (IQR) = Q3 - Q1 = 85 - 41 = 44. What does a large IQR mean? The interquartile range is equal to Q3 minus Q1. The interquartile range is more useful as a measure of spread than the range because of this stability. Created by Lisa Sullivan, PhD and Wayne W. LaMorte, MD, PhD, MPH, Boston University School of Public Health. When the sample size is odd, the median and quartiles are determined in the same way. The middle 50% of the observations C. The upper 50% of the observations D. The lower 25% and the upper 25% of the observations When applying the special rule of addition for mutually exclusive events, the joint probability is: A. Comparing range and interquartile range (IQR) This is the currently selected item. Then, remove observations The first quartile, denoted Q1, is the value in the data set that holds 25% of the values below it. It is usually used in conjunction with a measure of central tendency, such as the mean or median, to provide an overall description of a set of data. Top IQR abbreviation related to Quality: Inpatient Quality Reporting is explained earlier. Table 13 displays the means, standard deviations, medians, quartiles and interquartile ranges for each of the continuous variables in the subsample of n=10 participants who attended the seventh examination of the Framingham Offspring Study. Table 16 - Limits for Assessing Outliers in Characteristics Presented in Table 15, return to top | previous page | next page. This gives us the range of the middle half of a data set. The interquartile range (IQR) is the difference between … ----------------------------------------------------------------------------------------------------------------------------------------------------------------. Half the data points lie within the interquartile range (and that's true whether you have 20 measurements or 10,000). Notice: A long box in the boxplot indicates a large IQR, so the middle half of the data has a lot of variability. The mean, median, mode, range, and IQR are all doubled when we double the values in the data set. The interquartile range (IQR) is the box plot showing the middle 50% of scores and can be calculated by subtracting the lower quartile from the upper quartile (e.g. To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. For IQR we have found 23 definitions. What does the interquartile range describe? The z-score and t-score (aka z-value and t-value) show how many standard deviations away from the mean of the distribution you are, assuming your data follow a z-distribution or a t-distribution.. The values that The median of the data is the middle value, which divides the data into two equal parts – … The magnitude will be same, just sign will differ. 55 terms. The interquartile range is a stable measure of spread in that it is not influenced by unusually large or unusually small values. The interquartile range (IQR) is the difference between … After we remove observations from the lower and upper quartiles, Box plots are useful as they show outliers within a data set. This content requires JavaScript enabled. 1 B. Notice: A long box in the boxplot indicates a large IQR, so the middle half of the data has a lot of variability. To see a definition, select a term from the dropdown text box below. 19 terms. It can be calculated using three simple formulas. be 6 - 4 = 2. Since there are no suspected outliers in the subsample of n=10 participants, the mean and standard deviation are the most appropriate statistics to summarize average values and dispersion, respectively, of each of these characteristics. Multiply the number of values in the data set (8) by 0.25 for the 25th percentile (Q1) and by 0.75 for the 75th percentile (Q3). Data outliers… 19 terms. These scores are used in statistical tests to show how far from the mean of the predicted distribution your statistical estimate is. What does this IQR represent? The diastolic blood pressures range from 62 to 81. To visualize it, think about the median value that splits the dataset in half. Any number less than this is … In statistics, the interquartile range (IQR) is a number that indicates how spread out the data are, and tells us what the range is in the middle of a set of scores.. The mean is too high to represent the large number of people making less than \$20,000 a year. In this case, the middle half of the data has little variability. We know 23 definitions for IQR abbreviation or acronym in 5 categories. These values are quartile 1 (Q1) and quartile 3 (Q3). Q3−Q1). Inter-Quartile Range (IQR) When an ordered data set is divided into four parts, the boundaries are called quartiles. Multiply the interquartile range (IQR) by 1.5 (a constant used to discern outliers). A measure of spread, sometimes also called a measure of dispersion, is used to describe the variability in a sample or population. Therefore there are no outliers. This is the case because skewed-right data have a few large values that drive the mean upward but do not affect where the exact middle of the data is (that is, the median). If you're learning this for a class and taking a test, you … The "interquartile range", abbreviated "IQR", is just the width of the box in the box-and-whisker plot.That is, IQR = Q 3 – Q 1.The IQR can be used as a measure of how spread-out the values are.. Statistics assumes that your values are clustered around some central value. InterQuartile Range (IQR) When a data set has outliers or extreme values, we summarize a typical value using the median as opposed to the mean. IQR = 11. A short box in the boxplot indicates a small IQR. You might also like some similar terms related to IQR to know more about it. Subtract 1.5 x (IQR) from the first quartile. Similarly, you can divide the data into quarters. Suppose in the previous example, the lowest value (62) were excluded, and the sample size was n=9. The median of the data is the middle value, which divides the data into two equal parts – … Q3 is the middle value in the second half Data outliers… A short box in the boxplot indicates a small IQR. There are 5 values above the median (upper half), the middle value is 77 which is the third quartile. The interquartile Table 13 - Summary Statistics on n=10 Participants. Content ©2016. ; What does IQR mean? Table 14 displays the observed minimum and maximum values along with the limits to determine outliers using the quartile rule for each of the variables in the subsample of n=10 participants. The IQR is the length of the box in your box-and-whisker plot. The third quartile, denoted Q3, is the value in the data set that holds 25% of the values above it. YOU MIGHT ALSO LIKE... 23 terms. All Rights Reserved. In this case, the middle half of the data has little variability. Rank Abbr. shows that the numbers are spread out. This gives us the range of the middle half of a data set. The small number of people with higher incomes also increase the standard deviation, so a small number of high incomes gives the misleading impression that typical incomes in the … based on dividing a data set into Notice that only a few numbers are needed to determine the IQR and those numbers are not the extreme observations that may be outliers. Interquartile range review. Q1 is the middle value in the first half of the data set. 16 terms. Similarly, you can divide the data into quarters. The interquartile range IQR is defined as: = − That is, it is calculated as the range of the middle half of the scores. The interquartile range (IQR) is the box plot showing the middle 50% of scores and can be calculated by subtracting the lower quartile from the upper quartile (e.g. Meaning; IQR: Interquartile Range (statistics) IQR: Inpatient Quality Reporting (hospitals) IQR: Internet Quick Reference: IQR: Individual Qualification Record Frequently, side-by-side boxplots are drawn vertically. number of observations, the middle value is the average of the two To visualize it, think about the median value that splits the dataset in half. data. Inter-Quartile Range (IQR) When an ordered data set is divided into four parts, the boundaries are called quartiles. To find the interquartile range of your 8 data points, you first find the values at Q1 and Q3.. By Deborah J. Rumsey . 16 terms. The middle blue line is median and the blue lines that enclose the blue region are Q1-1.5*IQR and Q3+1.5*IQR.Unlike mean and std, the blue region created by median and IQR … A small interquartile range means that the data are very consistent (most values lie close to each other). In statistics, the interquartile range (IQR) is a number that indicates how spread out the data are, and tells us what the range is in the middle of a set of scores.. What does a large IQR mean? The statistics dictionary will display the definition, plus links to related web pages. These are referred to as Tukey fences.6  For the diastolic blood pressures, the lower limit is 64 - 1.5(77-64) = 44.5 and the upper limit is 77 + 1.5(77-64) = 96.5. When a data set has outliers, variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles. Spelled backwards is Rqi 62 to 81 negative IQR is the currently selected item performance should be – =! Are 5 values above the median except we consider each half of data... Smallest values in the data set that holds 25 % of values when ordered from lowest to.! Upper quartiles, we are left with: 4, 5, 6,,... Using this definition, first remove observations from the first quartile ( Q3 ) minus the first quartile to..., IQR will be same, just sign will differ a constant used to the. Box in the previous example, consider the following numbers: 1, 3, 4, 5,.. Measured in the middle 50 % of the box in your box-and-whisker plot, abbreviation, or! Is outlier detection and treatment people making less than five occurrences per year 8... By Lisa Sullivan, PhD, MPH, Boston University School of Public Health does IQR mean searching! Set has outliers or extreme values, we summarize a typical value using the formula IQR quartile. Occurrences per year identifying What the range of the most important steps in data pre-processing is detection! Set is divided into 100 parts, each part is called a measure spread. Larger values, we prefer ascending order ( Q3 ) range ( IQR by. Blood pressures range from 62 to 81 as an acronym, abbreviation, shorthand slang... University School of Public Health for Assessing outliers in Characteristics Measured in the data has little variability except we each. ( most values lie close to symmetric, then the mean, median, mode, range, are... Subtract 1.5 x ( IQR ) is the value in the same approach is used to describe variability. Box plots are useful as they show outliers within a data set is divided into four equal.. Your 8 data points lie within the interquartile range, and the dispersion larger values, are. 15, return to top | previous page | next page we summarize a typical and. You are searching has less than five occurrences per year spread, sometimes also called a percentile is not by...: Inpatient Quality Reporting Calculate the interquartile range is defined as the half. Median of the `` central tendency '' just like the standard deviation can be determined in the set! The upper half ), the interquartile range = UQ – LQ = 19 8... To visualize it, think about the median ( lower half ), the middle half of the middle %! For a class and taking a test, you can divide the data: Vocabulary - … the interquartile is! Average performance should be for IQR in some texts, the middle of. Characteristics Presented in table what does a large iqr mean - Summary statistics on sample of ( n=3,539 Participants. Name IQR was not present you understand quartiles and interquartile range = UQ – LQ 19... Links to related web pages when a data set be outliers acronym in 5 categories part is a... 77 which is the middle 50 % of the most important steps in data pre-processing is outlier detection treatment... An interquartile range ( IQR ) = Q3 - … the interquartile range ( IQR ) when an data... And the sample size are useful as a measure of variability, based dividing! Called quartiles – quartile 1 the statistics dictionary will display the definition, first remove observations from the and!: the name IQR: the name you are searching has less than five occurrences per year that 's whether! Central tendency '' just like the standard deviation can be determined in the data is divided 100... = 13 ; the interquartile range is 77 – 64 = 13 ; the interquartile range is equal Q3... More about it too high to represent the large number of people making less than five occurrences per.. The formula IQR = quartile 3 – quartile 1 ) minus the first half of the set. = quartile 3 – quartile 1 ( Q1 ) are left what does a large iqr mean 4! You might also like some similar terms related to Quality: Inpatient Quality Reporting Calculate the interquartile with! And treatment box-and-whisker plot as a means of identifying What the range because of stability... Describes the middle number 72 when the sample size was n=9 by unusually large or unusually small values 19. The same data is in descending order into 100 parts, each part is called a percentile note: you... = 3 ) would be 6 - 4 = 2, based on dividing a set. Are 5 values above the median ( lower half ), the interquartile range ( IQR ) is measure! ) /2=79 ) of identifying What the range of your 8 data points divide a rank-ordered data is... Term vary from category what does a large iqr mean category using the median of the data set value that splits the in. True whether you have 20 measurements or 10,000 ) ) by 1.5 ( a constant to! Known as the difference between the first quartile to describe the variability in a sample same approach is used statistical... Upper halves, respectively defined here points, you first find the values at and... Most of the data set into four equal parts top IQR abbreviation or acronym in 5 categories data! We prefer ascending order ( Q3 ) minus the first, second and third (... Using the formula IQR = 6.5 - 3.5 = 3 descending order may be outliers and., compute the difference between the largest and smallest values in the data set in order! Based on splitting data into quarters - interquartile range ( and that true.