Question

Q.4 Find the median class.

Size of the shoe No. of pair sold
3 4
4 18
5 25
6 12
7 5
8 1

Answer 1

Answer: Median = 5

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Step-by-step explanation

Given Table of Data

`\begin{array}c \cline{1-2}\text{Size of the shoe} & \text{No. of pair sold}\\\cline{1-2}3 & 4\\\cline{1-2}4 & 18\\\cline{1-2}5 & 25\\\cline{1-2}6 & 12\\\cline{1-2}7 & 5\\\cline{1-2}8 & 1\\\cline{1-2}\end{array}`

The second column is the set of frequencies. Adding up those frequencies gets us

4+18+25+12+5+1 = 65

There are 65 total shoes.

Divide this in half

65/2 = 32.5

There are 32 values below the median, and 32 values above it. That's 32+32 = 64 values so far. When including the median value itself we have 32+1+32 = 65 values total. This only works when the sample size is odd.

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What we'll do is add up the partial sums of the frequency values.

The goal is to get to a sum of 33, or larger, because the median is in the 33rd slot.

Adding the first two frequencies gets us 4+18 = 22. This is not 33 or larger, so we move on.

Adding the first three frequencies gets us 4+18+25 = 22+25 = 47 which is 33 or larger.

What this tells us is that the median corresponds to the third row of the table, since we added the first three frequencies to get to 33 or larger.

The median must be 5.