Calculate the standard deviation of below data 16,24,18,17,12,17,25,15,19,20,27,24
Answers
Answer:
1.99
Step-by-step explanation:
X f fx X-Mean f(X−x)
2
10 2 20 −4 32
11 7 77 −3 63
12 10 120 −2 40
13 12 156 −11 2
14 15 210 0 0
15 11 165 1 11
16 10 160 2 40
17 6 102 3 54
18 3 54 4 48
Total 76 fX=1064
f(X−X)
2
=300
−
X=
76
1064
=14
σx=
76
300
=
3.95
=1.99.
Answer:
Standard deviation (S.D) = 14.603
Step-by-step explanation:
Given data
16, 24, 18, 17, 12, 17, 25, 15, 19, 20, 27, 24
here we need to find standard deviation of the given data from mean
standard deviation of a data = ∑x²/ N
here ∑x² = sum of squares of deviations of the data
N = number of observations
⇒ mean of the data = [16+24+18+17+12+17+25+15+19+20+27+24]/ 12
= 234 / 12 = 19.5
⇒ now calculate deviations in following table
observations deviations squares of deviations
16 3.5 12.25
24 4.5 20.25
18 1.5 2.25
17 2.5 6.25
12 7.5 56.25
17 2.5 6.25
25 5.5 30.25
15 4.5 20.25
19 0.5 0.25
20 0.5 0.25
27 0.7 0.49
24 4.5 20.25
N = 12 ∑ x² = 175.24
standard deviation (S.D) = 175.24/ 12 = 14.603