Page 210 - Data Science class 10
P. 210
2
2
2
2
2
2
2
2
2
2
2
2
= 6 +4 +4 +3 +3 +2 +1 +1 +1 +1 +3 +6 +11 2
13
= 36 + 16 + 16 + 9 + 9 + 4 + 1 + 1 + 1 + 1 + 9 + 36 + 121
13
= 260
13
= 20
Hence, the population variance is 20.
10. Find the sample variance of the following dataset:
5, 8, 11, 3, 2, 10, 9, 11, 12, 3, 12, 18, 24, 26
Ans. Find the mean by adding all data values and divide by the sample size n.
(5 + 8 + 11 + 3 + 2 + 10 + 9 + 11 + 12 + 3 + 12 + 18 + 24 + 26)
Mean =
14
= 11
The sample variance is:
∑ n x – x ) 2
8 8 i= 1 ( 1
n –1
2
2
2
2
2
2
2
2
2
2
2
2
= (5–11) +(8–11) +(11–11) +(3–11) +(2–11) +(10–11) +(9–11) +(11–11) +(12–11) +(3–11) +(12–11) +(18–11) +(24–11) 2
13 – 1
2
2
2
2
2
2
2
2
2
2
2
2
2
= 6 + 3 + 0 + 8 + 9 + 1 + 2 + 0 + 1 + 8 + 1 + 7 + 13 + 15 2
13
= 36 + 9 + 64 + 81 + 1 + 4 + 1 + 64 + 1 + 49 + 169 + 225
13
= 704
13
= 54.153846
Hence, the population variance is 54.153846.
208 Touchpad Data Science-X

