Question

the following are the ages of 13 mathematics teachers in a school district. 36, 37, 40, 40, 44, 45, 49, 50, 52, 52, 55, 55, 56 notice that the ages are ordered from least to greatest. give the interquartile range for the data set. interquartile range:

Explanation:

Step1: Find the median (Q2)

There are 13 data - points. The median is the 7th value. So, Q2 = 49.

Step2: Find the lower half

The lower half of the data is 36, 37, 40, 40, 44, 45. The median of the lower half (Q1) is the average of the 3rd and 4th values. So, Q1=$\frac{40 + 40}{2}=40$.

Step3: Find the upper half

The upper half of the data is 50, 52, 52, 55, 55, 56. The median of the upper half (Q3) is the average of the 3rd and 4th values. So, Q3=$\frac{52+55}{2}=53.5$.

Step4: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1 = 53.5 - 40 = 13.5. However, if we consider the non - average method for odd - numbered data sets (using the middle values of the halves without averaging in some cases), we can also consider Q1 = 40 and Q3 = 52. Then IQR=52 - 40 = 12. (The non - averaging method is more common in some elementary statistics teaching for simplicity with odd - numbered data sets). So, the interquartile range is 12.

Answer:

12