Chapter B.2, Problem 11E

To determine

To calculate: the mean median mode of a given set of data

Answer to Problem 11E

The mean of the data is $315$ , the median is $310$ and the mode is $300$ .

Explanation of Solution

Given information :

The given set of data whose mean median and mode are to be found are:

  $420,210,310,310,480,160$

Formula used :

  $Mean=\frac{{\displaystyle \sum x}}{N}$

  $Median=\frac{{\left(\frac{n}{2}\right)}^{th}term+{\left(\frac{n}{2}+1\right)}^{th}term}{2}$

  $Mode=3median-2mean$

Calculation:

The given numbers are $420,210,310,310,480,160$ .

Substitute $6$ for N in the formula to find mean.

  $\begin{array}{c}Mean=\frac{420+210+310+310+480+160}{6}\\ =315\end{array}$

Now arrange the given data in ascending order

  $160,210,310,310,420,480$

Calculate median of the numbers:

  $Median=\frac{{\left(\frac{n}{2}\right)}^{th}term+{\left(\frac{n}{2}+1\right)}^{th}term}{2}$

Substitute $6$ for $n$ .

  $\begin{array}{c}Median=\frac{{\left(\frac{6}{2}\right)}^{th}term+{\left(\frac{6}{2}+1\right)}^{th}term}{2}\\ =\frac{3^{th}term+4^{th}term}{2}\end{array}$

Substitute $310$ for $3^{rd}term$ and $310$ for $4^{th}term$ .

  $\begin{array}{c}Median=\frac{310+310}{2}\\ =310\end{array}$

Calculate Mode of the data:

  $Mode=3median-2mean$

Substitute $315$ for mean and $310$ for median.

  $\begin{array}{c}Mode=3\times 310-2\times 315\\ =300\end{array}$

Hence, the mean of the data is $315$ , the median is $310$ and the mode is $300$ .