Respuesta :
Answer:
(a)Range = 96
(b)Variance=1059.36
(c)Standard Deviation =32.55
Step-by-step explanation:
(a)Range
- Highest Value = 97
- Lowest Value = 1
Range = Highest Value - Lowest Value
=97-1
=96
(b)Variance
The variance of a sample for ungrouped data is defined by the formula:
[tex]Variance, s^2 = \dfrac{\sum(x-\overline{x})^2}{n-1}[/tex]
First, we determine the mean of the sample data.
[tex]Mean = \dfrac{40 +39+ 8+ 82+ 25+ 53+ 97+ 1+ 28+ 41+ 94}{11} \\=\dfrac{508}{11}\\\\ \overline{x}=46.2[/tex]
[tex]\sum(x-\overline{x})^2=(40-46.2)^2 +(39-46.2)^2+ (8-46.2)^2+ (82-46.2)^2+ (25-46.2)^2+ (53-46.2)^2+ (97-46.2)^2+ (1-46.2)^2+ (28-46.2)^2+ (41-46.2)^2+ (94-46.2)^2\\\\=38.44+51.84+1459.24+1281.64+449.44+46.24+2580.64+2043.04+331.24+27.04+2284.84[/tex]
=10593.64
Therefore:
Variance, Variance,
[tex]Variance, s^2 = \dfrac{10593.64}{11-1}\\\\=1059.36[/tex]
(c)Standard Deviation
[tex]s=\sqrt{Variance}\\ =\sqrt{1059.36}\\s=32.55[/tex]
The results tell us that there is great variability in the number of jerseys of the player as evidenced by the high standard deviation and range.
