Chapter 13, Problem 1PT

To determine

The mean, mode and median ofthe ages of students at a picnic $7,8,7,9,8,10,11,7$ is to be estimated.

Answer to Problem 1PT

The mean, mode and median of $7,8,7,9,8,10,11,7$ are $8.38,7,8$ respectively.

Explanation of Solution

Given:

The ages of students at a picnic: $7,8,7,9,8,10,11,7$

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 system is calculated as:

  $\begin{array}{l}X=\frac{{\displaystyle \sum }}{n}\\ X=\frac{{\displaystyle \sum \left(7+8+7+9+8+10+11+7\right)}}{8}\\ X=\frac{62}{8}\\ X=8.375\\ X\approx 8.38\end{array}$

Median of given system is calculated as:

Take the given numbers from the least to greatest:

  $7,7,7,8,8,9,10,11$

Here is an even number of system, so take the mean of middle two numbers which nothing but a median of even data:

  $X=\frac{8+8}{2}=8$

So, the median of the even number system is $8$

Modeof given system is calculated as:

In the given number system, the number $7$ occurs most of times or $3$ times.

So, the number $7$ is modeof given system.

Conclusion:

Hence,the results of given ages of students at a picnic area system as:

Mean: $8.38$

Median: $8$

Mode: $7$