Chapter 10.5, Problem 2GP

To determine

To find mean median mode, range and standard deviation.

Answer to Problem 2GP

Mean=44

Median=44.4

Mode=48

Range=13.6

Standard deviation=4.23

Explanation of Solution

Given information:

63,47,54,60,55,46,51,60,58,50,56,60

Formula used:

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

Where, n=total number of terms,

  ${\displaystyle \sum _{i=1}^n{X}_i}$ = sum of all terms

Mode= most repeating numbers.

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

Range= maximum- minimum

Standard deviation, ${\sigma }_{}=\sqrt{\frac{{\displaystyle \sum _{}^{}{(x_i^{}-\mu )}^2}}{N}}$

Where $x_i^{}$ = each value from data

  $\mu$ =mean of data

  $N$ = size of data

Calculation:

After multiplying with 0.8,

New data is 50.4,37.6,43.2,48,44,36.8,40.8,48,46.4,40,44.8,48

Sort the number in ascending order,

36.8,37.6,40,40.8,43.2,44,44.8,46.4,48,48,48,

Mean is,

Substituting the value,

  $=\frac{50.4+37.6+43.2+48,44+36.8+40.8+48+46.4+40+44.8+48}{12}$

So,

  $=\frac{528}{12}$

On solving,

  $=44$

Hence, mean is 44

For Median,

Substituting values,

  $=\frac{{(\frac{12}{2})}^{th}+{(\frac{12}{2}+1)}^{th}}{2}$

Solving,

  $=\frac{6^{th}+7^{th}}{2}$

Substituting the values,

  $=\frac{44+44.8}{2}$

On solving,

  $=44.4$

Hence, median is 44.4.

For mode,

Substituting the value,

  $\mathrm{mod}e=48$

For Range, substituting the value,

  $=50.4-36.8$

On solving,

  $=13.6$

Hence, range is 13.6

For standard deviation,

values	Difference= $x_{}^{}-\mu$	( $x_{}^{}-\mu {)}^2$
50.4	6.4	40.96
37.6	-6.4	40.96
43.2	-0.8	0.64
48	4	16
44	0	0
36.8	-7.2	51.84
40.8	-3.2	10.24
48	4	16
46.4	2.4	5.76
40	-4	16
44.8	0.8	0.64
48	4	16
Total		215.04

Substituting values,

  ${\sigma }_{}=\sqrt{\frac{215.04}{12}}$

On solving,

  $\sigma =4.23$