Question

The numbers of regular season wins for 10 football teams in a given season are given below. Determine the​ range, mean,​ variance, and standard deviation of the population data set.

22​,

1010​,

1515​,

44​,

1515​,

66​,

1414​,

1010​,

22​,

1010

  

The range is

1313.

​(Simplify your​ answer.)

The population mean is

nothing.

Answer 1

Solution:

The formulas for mean, variance, and standard deviation for population are given as below:

Range = Maximum - Minimum

Population Mean = µ = ∑ X/n

Population Variance = σ² = ∑[ (X - µ)^2]/n

Population Standard deviation = σ = Sqrt(σ²) = Sqrt(Variance)

The calculation table is given as below:

No.	X	(X - µ)^2
1	2	46.24
2	2	46.24
3	4	23.04
4	6	7.84
5	10	1.44
6	10	1.44
7	10	1.44
8	14	27.04
9	15	38.44
10	15	38.44
Total	88	231.6

From above table, we have

Maximum = 15

Minimum = 2

Range = Maximum - Minimum

Range = 15 - 2

Range = 13

n = 10

Population Mean = µ = ∑ X/n = 88/10 = 8.8

Population Mean = 8.8

Population Variance = σ² = ∑[ (X - µ)^2]/n

Population Variance = σ² = 231.6 / 10

Population Variance = σ² = 23.16

Population Standard deviation = σ = Sqrt(σ²) = Sqrt(23.16) = 4.81248377

Population Standard deviation = 4.81248377