Chapter 13, Problem 10SGR

To determine

The mean, mode and median of grams of fat per serving $2,7,4,5,6,4,5,6,3,5$ is to be estimated.

Answer to Problem 10SGR

Grams of fat per serving $2,7,4,5,6,4,5,6,3,5$ has:

Mean: $4.7$

Median: $5$

Mode: $5$

Explanation of Solution

Given:

Grams of fat per serving: $2,7,4,5,6,4,5,6,3,5$

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 grams of fat per servingis calculated as:

  $\begin{array}{l}X=\frac{{\displaystyle \sum }}{n}\\ X=\frac{{\displaystyle \sum \left(2+7+4+5+6+4+5+6+3+5\right)}}{10}\\ X=\frac{47}{10}\\ X=4.7\end{array}$

Median of grams of fat per servingis calculated as:

Take the grams of fat per serving from the least to greatest:

  $2,3,4,4,5,5,5,6,6,7$

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

  $X=\frac{5+5}{2}=5$

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

Mode of grams of fat per serving is calculated as:

In the given number system, the number $5$ occurs $3$ times.

So, the number $5$ is modeof grams of fat per serving.

Conclusion:

Hence,the results of given grams of fat per serving are as:

Mean: $4.7$

Median: $5$

Mode: $5$