Question

range? calculate the range and interquartile range for the following set of scores from a continuous variable: 23, 13, 10, 8, 10, 9, 11, 12.

Explanation:

Step1: Arrange data in ascending order

$8,9,10,10,11,12,13,23$

Step2: Calculate the range

Range = Maximum - Minimum. Maximum value is 23 and minimum value is 8. So, Range = $23 - 8=15$

Step3: Find the median (Q2)

There are 8 data - points. Median is the average of the 4th and 5th ordered values. So, $Q2=\frac{10 + 11}{2}=10.5$

Step4: Find the lower half of data

The lower half of the data is $8,9,10,10$. The median of the lower half (Q1) is the average of the 2nd and 3rd ordered values in the lower - half. So, $Q1=\frac{9 + 10}{2}=9.5$

Step5: Find the upper half of data

The upper half of the data is $11,12,13,23$. The median of the upper half (Q3) is the average of the 2nd and 3rd ordered values in the upper - half. So, $Q3=\frac{12+13}{2}=12.5$

Step6: Calculate the inter - quartile range

Inter - quartile range (IQR)=$Q3 - Q1$. So, $IQR = 12.5-9.5 = 3$

Answer:

Range: 15; Inter - quartile range: 3