Respuesta :
Answer:
Variance is 5.2575
Range is 7.6
Arithmetic Mean is 13.85
Step-by-step explanation:
Given the sample:
10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6.
(A) To calculate Variance
- Find the mean of the numbers, let the mean be M = (Sum of samples)/(number of samples)
M = (10.6 + 12.6 + 14.8 + 18.2 + 12.0 + 14.8 + 12.2 + 15.6)/8
= 110.8/8
= 13.85
- Subtract M from each sample, and square the result.
(10.6 - 13.85)² = 10.5625
(12.6 - 13.85)² = 1.5625
(14.8 - 13.85)² = 0.9025
(18.2 - 13.85)² = 18.9225
(12.0 - 13.85)² = 3.4225
(14.8 - 13.85)² = 0.9025
(12.2 - 13.85)² = 2.7225
(15.6 - 13.85)² = 3.0625
- Finally, variance is
V = (10.5625 + 1.5625 + 0.9025 + 18.9225 + 3.4225 + 0.9025 + 2.7225 + 3.0625)/8
= 42.06/8
= 5.2575
(B) Range = (Highest number in the sample) - (lowest number in the sample)
R = 18.2 - 10.6
= 7.6
(C) Arithmetic mean is M, which we have obtained earlier in (A)
M = 13.85
Answer:
[tex]Variance = 5.2575[/tex]
[tex]Range = 5[/tex]
[tex]Mean = 13.85[/tex]
Step-by-step explanation:
Given:
10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6
Number of companies (n) = 8
Required
A. Calculate the variance.
B. Calculate the range.
C. Calculate the arithmetic mean.
Calculating the variance. ...
We start by calculating the mean of the given data
[tex]Mean = \frac{\sum x}{n}[/tex]
[tex]Mean = \frac{10.6 + 12.6+ 14.8+ 18.2+ 12.0+ 14.8+ 12.2+ 15.6}{8}[/tex]
[tex]Mean = \frac{110.8}{8}[/tex]
[tex]Mean = 13.85[/tex]
Subtract the mean from each data
[tex]10.6 - 13.85 = -3.25\\12.6 - 13.85 = -1.25\\14.8 - 13.85 = 0.95\\18.2 - 13.85 = 4.35\\12.0 - 13.85 = -1.85\\14.8 - 13.85 = 0.95\\12.2 - 13.85 = -1.65\\15.6 - 13.85 = 1.75[/tex]
Square these results
[tex](-3.25)^2 = 10.5625 \\(-1.25)^2 = 1.5625 \\0.95^2 = 0.9025\\4.35^2 = 18.9225\\(-1.85)^2 =3.4225 \\0.95^2 =0.9025 \\(-1.65)^2 =2.7225 \\1.75^2 =3.0625[/tex]
Add these results
[tex]10.5625 + 1.5625 + 0.9025 + 18.9225 + 3.4225 + 0.9025 + 2.7225 + 3.0625 =42.06[/tex]
Divide result by n
[tex]Variance = \frac{42.06}{8}[/tex]
[tex]Variance = 5.2575[/tex]
Calculating the range. ..
Range is calculated as thus
[tex]Range = Highest - Lowest[/tex]
From the given data;
[tex]Highest = 15.6; Lowest = 10.6[/tex]
So,
[tex]Range = 15.6 - 10.6[/tex]
[tex]Range = 5[/tex]
Calculating the arithmetic mean....
[tex]Mean = \frac{\sum x}{n}[/tex]
[tex]Mean = \frac{10.6 + 12.6+ 14.8+ 18.2+ 12.0+ 14.8+ 12.2+ 15.6}{8}[/tex]
[tex]Mean = \frac{110.8}{8}[/tex]
[tex]Mean = 13.85[/tex]
