Question

In the data set below, what is the interquartile range? 85,78,32,12,55,50,14,13,27,90

Answer 1

The interquartile range of the given data set is 61. This is calculated by first arranging the data in ascending order, then identifying the first and third quartile values, and finally, subtracting the first quartile from the third quartile.

Step-by-step explanation:

The interquartile range is a measure of statistical dispersion, or in simpler terms, it represents the range within which the middle half of a data set falls. The calculation involves finding the first quartile (Q1) and third quartile (Q3) values and subtracting Q1 from Q3. For the data set provided, let's follow these steps:

1. Arrange the data set in ascending order: 12,13,14,27,32,50,55,78,85,90
2. Identify Q1 and Q3. Since there are 10 values in this set, Q1 is the average of the 2nd and 3rd values (14, 27) and Q3 is average of the 8th and 9th values (78, 85). So Q1 = 20.5 and Q3 = 81.5
3. Subtract Q1 from Q3 to get the interquartile range: 81.5 - 20.5 = 61

So the interquartile range of this data set is 61.

Learn more about Interquartile Range