Chapter 11.6, Problem 8PPSE

Solution

Tocalculate:The mean, median and mode of the data set shown below:

Age (years)	13	14	15	16	17	18	19
Frequency	7	12	18	9	5	4	2

The mean is 15.23, mode is 15, and median is 15.

Given information:

The given data set is:

Age (years)	13	14	15	16	17	18	19
Frequency	7	12	18	9	5	4	2

Formula used:

  $Mean=\frac{\text{Sum of data values}}{\text{Total number of data values}}$

Calculation:

Consider the given information.

Multiply the age and frequency as shown:

Age ( x )	13	14	15	16	17	18	19
Frequency( f )	7	12	18	9	5	4	2	$\sum f=57$
x f	91	168	270	144	85	72	38	$\sum xf=868$

  $\begin{array}{c}Mean=\frac{\sum xf}{\sum f}\\ =\frac{868}{57}\\ =15.23\end{array}$

Median is the middle value of the ordered data set. So median of the given data set will be data value at $\frac{57+1}{2}={29}^{th}$ position.

From the table the data value at 29^th position is 15. So, the median of the data set is 15.

Mode is the highest frequency value of the given data set. It can be observed that the frequency of 15 is 18, which is the highest among all.

So, the mode of the data set is 15.