Question

1. 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. Here, Maximum = 23, Minimum = 8. So, Range = $23 - 8=15$

Step3: Find the median (Q2)

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

Step4: Find the lower half and Q1

The lower half of the data is $8,9,10,10$. The median of the lower half (Q1) is $\frac{9+10}{2}=9.5$

Step5: Find the upper half and Q3

The upper half of the data is $11,12,13,23$. The median of the upper half (Q3) is $\frac{12 + 13}{2}=12.5$

Step6: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1. So, IQR=$12.5−9.5 = 3$

Answer:

Range: 15, Inter - quartile range: 3