Question

find each measure for the given set of data: 11, 13, 17, 20, 22, 25, 27, 31, 31, 33
mean =
median =
range =
interquartile range =
14
17
19
21

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 10$ and $\sum_{i=1}^{10}x_{i}=11 + 13+17+20+22+25+27+31+31+33=240$. So $\bar{x}=\frac{240}{10}=24$.

Step2: Calculate the median

Since $n = 10$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. The $\frac{10}{2}=5$th value is $22$ and the $6$th value is $25$. So the median $M=\frac{22 + 25}{2}=23.5$.

Step3: Calculate the range

The range $R=x_{\max}-x_{\min}$, where $x_{\max}=33$ and $x_{\min}=11$. So $R=33 - 11=22$.

Step4: Calculate the inter - quartile range

First, find the lower half and upper half of the data. The lower half is $11,13,17,20,22$ and its median (first quartile $Q_1$) is $17$. The upper half is $25,27,31,31,33$ and its median (third quartile $Q_3$) is $31$. The inter - quartile range $IQR=Q_3 - Q_1=31 - 17 = 14$.

Answer:

Mean = 24
Median = 23.5
Range = 22
Interquartile range = 14