To see a definition, select a term from the dropdown text box below. The statistics dictionary will display the definition, plus links to related web pages. The interquartile range IQR is a measure of variability, based on dividing a data set into quartiles.
Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively. For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, The data and the interquartile range are displayed on the dot plot below.
See: lower quartile , measure of spread , quartiles , upper quartile. Curriculum achievement objectives references Statistical investigation: Levels 5 , 6 , 7 , 8.
Use the resource finder. The interquartile range is Lastly, our interquartile range is , so is our interquartile range. To find the IQR, we first must find the and , because. In data sets, is defined as the median of the top half of the data and is defined as the median of the bottom half of the data. In a previous problem, we placed the data pieces in numerical order:.
Our upper half of our data set, the numbers above our median, now consists of. The median, or middle number, of this upper half is , our. The lower half of data, numbers below our median, is , with being our median,. We now have our and our. Thus our. In data sets, is defined as the median of the top half of data and is defined as the median of the bottom half of the data. The lower half of data, numbers below our median, is with being our median,.
Note that although we have an outlier of , our. Therefore, we can observe that an outlier's effect on a data set is not very strong when finding the interquartile range. This question is asking for the IQR which is , which is. The Interquartile range, or IQR, is defined as the. The first step is the find the median of the data set, which in this case is. This number is what cuts the data set into two smaller sets, an upper quartile and lower quartile. When we subtract from we end up with as our IQR.
To find the IQR, we must first find the and. The is the median of the upper quartile, the numbers above the median:. Now we need to divide the data set into the upper quartile and lower quartile, we do so by finding the mean which is the center value of the data set. In this data set, our median is. This means that our upper quartile consists of. Thus, our IQR is. If you've found an issue with this question, please let us know.
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Possible Answers:. Correct answer:. Explanation : How do you find the interquartile range? We can find the interquartile range or IQR in four simple steps: Order the data from least to greatest Find the median Calculate the median of both the lower and upper half of the data The IQR is the difference between the upper and lower medians Step 1: Order the data In order to calculate the IQR, we need to begin by ordering the values of the data set from the least to the greatest.
Let's sort an example data set with an odd number of values into ascending order. Rearrange into ascending order. Step 2: Calculate the median Next, we need to calculate the median. Cross out values until you find the centermost point The median of the odd valued data set is four. Find the average of the two centermost values. The median of the even valued set is four. Step 3: Upper and lower medians Once we have found the median of the entire set, we can find the medians of the upper and lower portions of the data.
Omit the centermost value. Find the median of the lower portion. Calculate the average of the two values. The median of the lower portion is Find the median of the upper portion. The median of the upper potion is If the data set has an even number of values, we will use the two values used to calculate the original median to divide the data set. The median of the lower portion is two.
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