Chapter 10.5, Problem 1GP

To determine

To find mean median mode, range and standard deviation.

Answer to Problem 1GP

Mean=30

Median=32.5

Mode=22

Range=38

Standard deviation=10.14

Explanation of Solution

Given information: Data set is,

27,41,15,36,26,40,53,38,37,24, 45, 26

Formula used: Mean formula is,

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 formula is,

Mode= most repeating numbers.

Median formula is,

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

Range formula is,

Range= maximum- minimum

Standard deviation formula is,

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

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

  $\mu$ =mean of data

  $N$ = size of data

Calculation:

After adding -4,

New data is 23,37,11,32,22,36,49,34,33,20,41,22

Sort the number in ascending order,

11,20,22,22,23,32,33,34,36,37,41,49

For mean.

Substituting the value,

  $mean=\frac{23+37+11+32+22+36+49+34+33+20+41+22}{12}$

So,

  $mean=\frac{360}{12}$

  $mean=30$

For median.

Substituting value,

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

Substituting the values,

  $=\frac{32+33}{2}$

On solving,

  $=32.5$

For mode, substituting the value

Mode= 22

For Range,

Substituting the values,

  $range=49-11$

On solving,

  $range=38$

For standard deviation,

values	Difference= $x_{}^{}-\mu$	( $x_{}^{}-\mu {)}^2$
11	-19	361
20	-10	100
22	-8	64
22	-8	64
23	-7	49
32	2	4
33	3	9
34	4	16
36	6	36
37	7	49
41	11	121
49	19	361
Total		1234

Substituting value,

  ${\sigma }_{}=\sqrt{\frac{1234}{12}}$

On solving,

  $\sigma {=}_{}10.14$