find the interquartile range of the data set below. 26, 33, 43, 25, 35, 46, 37, 31, 28, 37

Explanation:

Step1: Sort the data set

Sort the data set (26,33,43,25,35,46,37,31,28,37) in ascending order: (25,26,28,31,33,35,37,37,43,46)

Step2: Find the median

Since there are (n = 10) data points, the median is the average of the (5^{th}) and (6^{th}) values. The median (Q_2=\frac{33 + 35}{2}=34)

Step3: Find (Q_1) and (Q_3)

The lower half of the data is (25,26,28,31,33). The median of the lower half ((Q_1)) is the (3^{rd}) value. So (Q_1 = 28) The upper half of the data is (35,37,37,43,46). The median of the upper half ((Q_3)) is the (3^{rd}) value. So (Q_3=37)

Step4: Calculate the inter - quartile range (IQR)

The formula for the inter - quartile range is (IQR=Q_3 - Q_1) Substitute (Q_1 = 28) and (Q_3=37) into the formula: (IQR=37 - 28)

Answer:

(9)