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dangina [55]
3 years ago
10

Find the sample Standard deviation and the population standard deviation of the data set 17,37,56,16,12,16,19,45,14,37,21,26,43,

46,42
Mathematics
1 answer:
makvit [3.9K]3 years ago
6 0

Answer:

1. 13.98

2. 14.47

Step-by-step explanation:

The question is on sample standard deviation and population standard deviation

<u>Arrange the data in increasing order</u>

12,14, 16,16,17,19,21,26,35,37,42,43,45,46,56

n=15

<u>Find the mean of the data set</u>

<u />

mean = (12+14+ 16+16+17+19+21+26+35+37+42+43+45+46+56)/15

mean= 29.67 ⇒30

<u>Find the deviations</u>

You subtract the value of mean from each of  the data set given

Deviations= -18, -16, -14, -14, -13,-11, -9,-4,5,7,12,13,15,16,26

<u>Find squares of deviations</u>

= 324, 256, 196, 196, 169, 121, 81, 16, 25, 49, 144, 196, 225, 256, 676

<u>Find sum of squares of deviations</u>

324+ 256+ 196+ 196+ 169+ 121+ 81+ 16+ 25+ 49+ 144+ 196+ 225+ 256+ 676 = 2930

1. Treating the data set to represent an entire population then;

Variance= sum of squares of deviation/number of data set

Variance= 2930/15 = 195.33

Population standard deviation = √195.33 = 13.98

2. Treating the data set as a sample , the number of data set is reduced by one.i.e n= 15-1= 14

Sample Variance=2930/14 =209.29

sample standard deviation= √209.29 = 14.47

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