Chapter 13, Problem 11SGR

To determine

The mean, mode and median of inches of rain last week $1.5,2,2.5,2,1.5,2.5,3$ is to be estimated.

Answer to Problem 11SGR

Inches of rain last week $1.5,2,2.5,2,1.5,2.5,3$ has:

Mean: $2.14$

Median: $2$

Mode: $1.5,2,2.5$

Explanation of Solution

Given:

Inches of rain last week: $1.5,2,2.5,2,1.5,2.5,3$

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 inches of rain last week is calculated as:

  $\begin{array}{l}X=\frac{{\displaystyle \sum }}{n}\\ X=\frac{{\displaystyle \sum \left(1.5+2+2.5+2+1.5+2.5+3\right)}}{7}\\ X=\frac{15}{7}\\ X=2.1428\\ X\approx 2.14\end{array}$

Median of inches of rain last week is calculated as:

Take the inches of rain last weekfrom the least to greatest:

  $1.5,1.5,2,2,2.5,2.5,3$

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 $2$

Modeof inches of rain last week is calculated as:

In the given number system, the numbers $1.5,2,2.5$ occurs $2$ times.

So, the numbers $1.5,2,2.5$ is mode of inches of rain last week.

Conclusion:

Hence,the results of giveninches of rain last week are as:

Mean: $2.14$

Median: $2$

Mode: $1.5,2,2.5$