Respuesta :
Variance is given by s^2 = [summation (x - mean)^2] / n.
mean = (90 + 75 + 72 + 88 + 85) / 5 = 82
Variance = [(90 - 82)^2 + (75 - 82)^2 + (72 - 82)^2 + (88 - 82)^2 + (85 - 82)] / 5
= [8^2 + (-7)^2 + (-10)^2 + 6^2 + 3^2] / 5
= (64 + 49 + 100 + 36 + 9] / 5
= 258 / 5
=258.
mean = (90 + 75 + 72 + 88 + 85) / 5 = 82
Variance = [(90 - 82)^2 + (75 - 82)^2 + (72 - 82)^2 + (88 - 82)^2 + (85 - 82)] / 5
= [8^2 + (-7)^2 + (-10)^2 + 6^2 + 3^2] / 5
= (64 + 49 + 100 + 36 + 9] / 5
= 258 / 5
=258.
Answer:
The value of the numerator of the calculation of the variance= 258
and Variance= 51.6
Step-by-step explanation:
We know that in order to calculate the variance we need to follow following steps:
- First calculate mean.
- Then subtract each of the data points from means and square the difference quantity.
- Lastly calculate the mean of these squared quantity.
The data points are:
90, 75, 72, 88, 85
The mean of these data points are:
[tex]Mean=\dfrac{90+75+72+88+85}{5}\\\\\\Mean=\dfrac{410}{5}\\\\\\Mean=82[/tex]
Now on finding the difference terms i.e.
90-82=8
75-82= -7
72-82= -10
88-82=6
and 85-82=3
The square of these difference term is:
8²=64
(-7)²=49
(-10)²=100
6²=36
and 3²=9
Hence, the mean of these squared quantity i.e. Variance is:
[tex]Variance=\dfrac{64+49+100+36+9}{5}\\\\\\Variance=\dfrac{258}{5}\\\\\\Variance=51.6[/tex]
