Question

bloomington counted how many times people used the public pool last month. going swimming last month what is the median of the numbers? submit

Explanation:

Step1: Count the total number of data points

Count the number of X's. There is 1 X for 1, 1 X for 2, 2 X's for 3, 2 X's for 4, 6 X's for 5. So total number of data points \(n=1 + 1+2 + 2+6=12\) (an even - numbered data set).

Step2: Find the position of the median

For an even - numbered data set \(n = 12\), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=\frac{12}{2}=6\) and \(\frac{n}{2}+1 = 7\).

Step3: List out the data in order

List the data: \(1,2,3,3,4,4,5,5,5,5,5,5\) (1 one, 1 two, 2 threes, 2 fours, 6 fives). The 6th value is 4 and the 7th value is 5.

Step4: Calculate the median

The median \(M=\frac{4 + 5}{2}=4.5\)

Answer:

\(4.5\)