Chapter 13.1, Problem 7PPS

To determine

To calculate: The mean, median and mode of the set of data.

Answer to Problem 7PPS

Mean $=245$ , Median $=242.5$ , Mode $=200$ .

Explanation of Solution

Given information:

The set of data is 250,200,320,235,265,200.

Formula used:

Mean $=\frac{{\displaystyle \sum _{i=1}^n{x}_i}}{n}$ ,

Median $={(\frac{n+1}{2})}^{th}term$ , if n is odd.

Median $=\frac{{(\frac{n}{2})}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$ , if n is even.

Mode $=$ most frequently occurring data

n $=$ number of terms.

Calculation:

The set of data 250,200,320,235,265,200

Arranging in ascending order,

200,200,235,250,265,320

Here, $n=6$ , which is even.

Mean $=\frac{200+200+235+250+265+320}{6}=\frac{1470}{6}=245$

Median $=\frac{{(\frac{n}{2})}^{th}term+{(\frac{n}{2}+1)}^{th}term}{2}$$=\frac{{(\frac{6}{2})}^{th}term+{(\frac{6}{2}+1)}^{th}term}{2}$

  $\begin{array}{l}=\frac{3^{rd}term+4^{th}term}{2}\\ =\frac{235+250}{2}\\ =\frac{485}{2}\\ =242.5\end{array}$

In the data set 200 occurred 2 times.

Thus, Mode $=200$

Conclusion:

Mean $=245$ , Median $=242.5$ , Mode $=200$ .