Chapter 10.3, Problem 14PPS

a.

To determine

To find mean and standard deviation

Answer to Problem 14PPS

Mean is 1155 and Standard deviation is 50.05

Explanation of Solution

Given information:

15th annual 5k road race
Place	Time(min: s)	place	Time(min: s)	Place	Time(min: s)
1	17.51	6	19.03	11	19.50
2	18.01	7	19.06	12	20.07
3	18.17	8	19.27	13	20.11
4	18.22	9	19.49	14	20.13
5	18.26	10	19.49	15	20.13

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 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:

Converting the values into seconds,

15th annual 5k road race
Place	Time( s)	place	Time(s)	Place	Time(s)
1	1071	6	1143	11	1190
2	1081	7	1146	12	1207
3	1097	8	1167	13	1211
4	1102	9	1189	14	1213
5	1106	10	1189	15	1213

For mean substituting values,

  $=\frac{\text{1071+1081+1097+1102+1106+1143+1146+1167+1189+1189+1190+1207+1211+1213+1213}}{15}$

So,

  $=\frac{17325}{15}$

On solving,

  $=1155$

Hence, mean is 1155.

Values	Difference= $x_{}^{}-\mu$	${(x_{}^{}-\mu )}^2$
1071	-84	7056
1081	-74	5476
1097	-58	3364
1102	-53	2809
1106	-49	2401
1143	-12	144
1146	-9	81
1167	12	144
1189	34	1156
1189	34	1156
1190	35	1225
1207	52	2704
1211	56	3136
1213	58	3364
1213	58	3364
Total	37580

For Standard deviation substituting values,

  ${\sigma }_{}=\sqrt{\frac{37580}{15}}$

On solving,

  $\sigma$ =50.05

Hence, standard deviation is 50.05

b.

To determine

To identify sample and population.

Explanation of Solution

Given information:

15th annual 5k road race
Place	Time(min: s)	place	Time(min: s)	Place	Time(min: s)
1	17.51	6	19.03	11	19.50
2	18.01	7	19.06	12	20.07
3	18.17	8	19.27	13	20.11
4	18.22	9	19.49	14	20.13
5	18.26	10	19.49	15	20.13

Here, sample is equal as population because we applied mean and standard deviation to all the data set. The main difference between a population and sample has to do with how observations are assigned to the data set. A population includes all of the elements from a set of data. A sample consists one or more observations drawn from the population.

c.

To determine

To analyse the sample.

Explanation of Solution

Given information:

15th annual 5k road race
Place	Time(min: s)	place	Time(min: s)	Place	Time(min: s)
1	17.51	6	19.03	11	19.50
2	18.01	7	19.06	12	20.07
3	18.17	8	19.27	13	20.11
4	18.22	9	19.49	14	20.13
5	18.26	10	19.49	15	20.13

After analysing, the data is classified as quantitative as it can be measured and can be researched on, on qualitative, we cannot do mathematical operations