Chapter B.2, Problem 14E

To determine

To calculate:

Mean mode and median of the given data set.

Answer to Problem 14E

Mean, mode and median of the given data set is $3.08040,3,3$ respectively.

Explanation of Solution

Given information:

Number of girls	$0$	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$0$	$24$	$45$	$54$	$50$	$19$	$7$

Numbers of families in the study with the indicated numbers of girls given as below:

Number of girls	$0$	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$0$	$24$	$45$	$54$	$50$	$19$	$7$

The average of given data set having $n$ numbers is the sum of the numbers divided by $n$ .

So mean is calculated as,

  $\begin{array}{l}\overline{x}=\frac{\left(0.0\right)+\left(1.24\right)+\left(2.45\right)+\left(3.54\right)+\left(4.50\right)+\left(5.19\right)+\left(6.7\right)}{0+24+45+54+50+19+7}\\ \overline{x}=\frac{613}{199}\\ \overline{x}=3.08040\end{array}$

Thus, mean is $3.08040$ .

To find out the median of the given data need to first make a cumulative frequency table:

Numbers of girls	Frequency	Cumulative frequency
$0$	$0$	$0$
$1$	$24$	$25$
$2$	$45$	$70$
$3$	$54$	$124$
$4$	$50$	$174$
$5$	$19$	$193$
$6$	$7$	$200$

The colored line denotes the median row of the data.

Thus, the median of the data is $3$ .

The data $54$ has the highest frequency.

Therefore, mode of the data is $3$ .