find the median and mean of the data set with the outlier included. books checked out from school library…

Explanation:

Step1: List out the data

From the dot - plot, the data set is {5, 55, 55, 60, 60, 60, 65, 65, 65, 70, 70, 75}. There are (n = 12) data points.

Step2: Calculate the median

Since (n = 12) (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. (\frac{n}{2}=6) and (\frac{n}{2}+1 = 7). The 6th value is 60 and the 7th value is 65. Median(=\frac{60 + 65}{2}=\frac{125}{2}=62.5).

Step3: Calculate the mean

The mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}). (\sum_{i=1}^{12}x_{i}=5+55+55+60+60+60+65+65+65+70+70+75=705). Mean(=\frac{705}{12}=58.75).

Answer:

Median: 62.5 books Mean: 58.75 books