Chapter 13, Problem 2PT

To determine

The mean, mode and median of shoes sizes $4,5,6,5,4,7,6$ is to be estimated.

Answer to Problem 2PT

The shoes size system $4,5,6,5,4,7,6$ has:

Mean: $5.29$

Median: $5$

Mode: $4,5,6$

Explanation of Solution

Given:

Shoe sizes: $4,5,6,5,4,7,6$

Concept Used:

Mean is given by the following expression:

  $X=\frac{{\displaystyle \sum }}{n}$

Where,

Sum of data point: ${\displaystyle \sum }$

Number of data point: $n$

Median:

To find the median of the data points, the arrangement of numbers from the least to greatest has to be used.

For the even number of system, the mean of middle two numbers has to calculated which nothing but a median of even data

In case of odd numbers system take middle one number which is the median of system.

Mode:

The number which occurs most of times in the system is known as the mode.

Calculation:

Mean of the given shoes size systemis calculated as:

  $\begin{array}{l}X=\frac{{\displaystyle \sum }}{n}\\ X=\frac{{\displaystyle \sum \left(4+5+6+5+4+7+6\right)}}{7}\\ X=\frac{37}{7}\\ X=5.285\\ X\approx 5.29\end{array}$

Median of givenshoes size system is calculated as:

Take the given numbers from the least to greatest:

  $4,4,5,5,6,6,7$

Here is an odd number of system, so take the middle one number which nothing but a median of odd data.

So, the median of the odd number system is $5$

Mode of given shoes size system is calculated as:

In the given number system, the number $4,5,6$ occurs $2$ times.

So, the numbers $4,5,6$ is mode of given shoes size system.

Conclusion:

Hence,the results of given shoes size system are as:

Mean: $5.29$

Median: $5$

Mode: $4,5,6$