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:
<u><em>Step(i):-</em></u>
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⁻ = ![\frac{116.8+115.7+114.9+115.4+115.9}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B116.8%2B115.7%2B114.9%2B115.4%2B115.9%7D%7B5%7D)
Mean of sample x⁻ = 115.74
<u><em>Step(ii):- </em></u>
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
![S^{2} = \frac{1.1236+0.0016+0.7056+0.1156+0.0256}{5-1} = 0.493](https://tex.z-dn.net/?f=S%5E%7B2%7D%20%3D%20%5Cfrac%7B1.1236%2B0.0016%2B0.7056%2B0.1156%2B0.0256%7D%7B5-1%7D%20%3D%200.493)
The variance of the sample S² = 0.493
The standard deviation of the sample S =√0.493 = 0.7021