Question

here are the ages of 13 people in a coffee shop on a given day: 26, 44, 22, 28, 55, 32, 15, 39, 54, 69, 21, 18, 48 identify the third quartile by finding the middle number on the right side of the median. if there is no middle number, average the two middle numbers. 15, 18, 21, 22, 26, 28, 32, 39, 44, 48, 54, 55, 69 first quartile (q₁) median (q₂) third quartile (q₃) 21.5 ?

Explanation:

Step1: Locate the median

The data set has 13 numbers. The median (Q2) is the 7th number. After sorting: 15, 18, 21, 22, 26, 28, 32, 39, 44, 48, 54, 55, 69. The median is 32.

Step2: Consider the data on the right - hand side of the median

The data on the right - hand side of 32 is: 39, 44, 48, 54, 55, 69.

Step3: Calculate the third quartile

Since there are 6 numbers (an even count), we average the 3rd and 4th numbers. The formula for the average of two numbers \(a\) and \(b\) is \(\frac{a + b}{2}\). Here \(a = 48\) and \(b = 54\). So \(Q3=\frac{48 + 54}{2}=\frac{102}{2}=51\)

Answer:

51