Question

1. mia decided she wanted to go back to school shopping online. she looked at a variety of clothing items and found the following prices: $9 $11 $11 $12 $14 $14 $18 $18 $18 $18 $23 $23 $23 $25 $25 $25 $25 $25 $25 $30 $30 $31 $31 $35 $40 $40 $40 a. what is the median price? b. what is the percentile rank of clothing items that are $14? a. what is the percentile rank of clothing items that are $31?

Explanation:

Step1: Count data points

There are 28 data - points.

Step2: Find median position

For \(n = 28\) (even number of data - points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values. \(\frac{n}{2}=\frac{28}{2}=14\) and \(\frac{n}{2}+1 = 15\).

Step3: Order data (already ordered) and find median

The 14th value is \(25\) and the 15th value is \(25\). Median\(=\frac{25 + 25}{2}=25\).

Step4: Calculate percentile rank of \(14\)

Count the number of values less than or equal to \(14\). There are 6 values less than or equal to \(14\). Percentile rank\(=\frac{6}{28}\times100\approx21.43\).

Step5: Calculate percentile rank of \(31\)

Count the number of values less than or equal to \(31\). There are 20 values less than or equal to \(31\). Percentile rank\(=\frac{20}{28}\times100\approx71.43\).

Answer:

a. \(25\)
b. Approximately \(21.43\)
c. Approximately \(71.43\)