Answer:
a) The deviations from the mean
|x-x⁻| : 1.06 |-0.04 | |-0.84 | |-0.34 | | 0.16 |
b)
The variance of the sample S² = 0.493
The standard deviation of the sample S =√0.493 = 0.7021
Step-by-step explanation:
Step(i):-
Given that the sample observations
x : 116.8 115.7 114.9 115.4 115.9
Mean of the sample
= ∑ x/n
Mean of sample x⁻ = [tex]\frac{116.8+115.7+114.9+115.4+115.9}{5}[/tex]
Mean of sample x⁻ = 115.74
Step(ii):-
The deviations from the mean
|x-x⁻| : 116.8-115.74 115.7-115.74 114.9-115.74 115.4-115.74 115.9-115.74
|x-x⁻| : 1.06 |-0.04 | |-0.84 | |-0.34 | | 0.16 |
|x-x⁻||²: 1.1236 0.0016 0.7056 0.1156 0.0256
The variance of the given sample observations
S² = ∑ (x-x⁻)² / n-1
[tex]S^{2} = \frac{1.1236+0.0016+0.7056+0.1156+0.0256}{5-1} = 0.493[/tex]
The variance of the sample S² = 0.493
The standard deviation of the sample S =√0.493 = 0.7021
