Chapter 13, Problem 9SGR

To determine

The mean, mode and median of students numbers in each math class $22,23,24,22,21$ is to be estimated.

Answer to Problem 9SGR

The student’s numbers in each math class $22,23,24,22,21$ has:

Mean: $22.4$

Median: $22$

Mode: $22$

Explanation of Solution

Given:

Student’s numbers in each math class: $22,23,24,22,21$

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 student’s numbers in each math class is calculated as:

  $\begin{array}{l}X=\frac{{\displaystyle \sum }}{n}\\ X=\frac{{\displaystyle \sum \left(22+23+24+22+21\right)}}{5}\\ X=\frac{112}{5}\\ X=22.4\end{array}$

Median of student’s numbers in each math class is calculated as:

Take the student’s numbers in each math class from the least to greatest:

  $21,22,22,23,24$

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 oddnumber system is $22$

Modeof student’s numbers in each math classis calculated as:

In the given number system, the number $22$ occurs $2$ times.

So, the number $22$ is modeof student’s numbers in each math class.

Conclusion:

Hence,the results of givenstudent’s numbers in each math classare as:

Mean: $22.4$

Median: $22$

Mode: $22$