Question

Find the median

Age ​0-9, ​10-19,20-29, ​30-39, ​40-49, ​50-59, 60-69, 70-79, 80-89
Frequency 20, 29, 22, 28, 16, 59, 40, 17, 4

Answer 1

Answer: Somewhere between 50 and 59

Step-by-step explanation

Given Data

`\begin{array}c \cline{1-2}\text{Age} & \text{Frequency}\\\cline{1-2}0-9 & 20\\\cline{1-2}10-19 & 29\\\cline{1-2}20-29 & 22\\\cline{1-2}30-39 & 28\\\cline{1-2}40-49 & 16\\\cline{1-2}50-59 & 59\\\cline{1-2}60-69 & 40\\\cline{1-2}70-79 & 17\\\cline{1-2}80-89 & 4\\\cline{1-2}\end{array}`

Add up the frequency values to get the sample size.

n = sample size = number of people

n = sum of frequency values

n = 20+29+22+28+16+59+40+17+4

n = 235

Because n is odd, this will indicate the median is found at slot (n+1)/2 = (235+1)/2 = 118. There are 117 values below the median and 117 values above it. That gives 117+1+117 = 235 values total.

Compute the following partial sums:

• sum of first 2 terms: 20+29= 49
• sum of first 3 terms: 20+29+22 = 71
• sum of first 4 terms: 20+29+22+28 = 99
• sum of first 5 terms: 20+29+22+28+16 = 115
• sum of first 6 terms: 20+29+22+28+16+59 = 174

We stop once we either a) reach 118, or b) exceed 118.

Adding the first 5 terms gets us just under the goal of 118. Adding the first 6 terms gets us over the goal.

This tells us that the median age is somewhere in the age interval 50-59 as this is the 6th age group when starting from the top.

Somewhere in the interval "50-59" is slot 118 which is the median's position.

We don't know the actual median itself. We cannot nail it down to a single number. The best we can do is say "the median age is somewhere between 50 and 59".