Math help please

Question

3)

A random sample of 10 subjects have weights with a standard deviation of

9.4582

kg. What is the variance of their​ weights? Be sure to include the appropriate units with the result.

Units can be kg, kg^2 or kg^3

4) Below are the jersey numbers of 11 players randomly selected from a football team. Find the​ range, variance, and standard deviation for the given sample data. What do the results tell​ us?

65   49   38   52   18   66   7   78   34   57   39

  

Range =

Listed below are the top 10 annual salaries​ (in millions of​ dollars) of TV personalities. Find the​ range, variance, and standard deviation for the sample data. Given that these are the top 10​ salaries, do we know anything about the variation of salaries of TV personalities in​ general?

38     

37     

35     

29     

20     

19     

17     

15     

14.7     

13.3

  

The range of the sample data is

​?

Answer 1

(3) Variance is simply the square of standard deviation:

s = 9.4582 kg

s² ≈ 89.4575 kg²

(4)

x x-x̅ (x-x̅)²

65 19.273 371.438

49 3.273 10.711

38 -7.727 59.711

52 6.273 39.347

18 -27.727 768.802

66 20.273 410.983

7 -38.727 1499.802

78 32.273 1041.529

34 -11.727 137.529

57 11.273 127.074

39 -6727 45.256

----------------------------------------------------

Σ 503 4512.182

For mean (x̅):

x̅ = 45.727

n = 11

For variance:

s² = Σ(x-x̅)² / (n-1) = 4512.182 / 9 ≈ 451.218

s = √s² ≈ 21.242

Range (R):

R = max-min = 78-7 = 71

Both variance and standard deviation are measures of variability of the data. It tells you the degree of spread of the data. If you try to change the minimum and/or maximum and make it closer to the mean, then both variance and standard deviation are going to be smaller in value. However, the data is considered as qualitative. The numbers are very insignificant for computation because it only identifies a person. The Jersey number 7, for example, doesn't mean he is the weakest or the smallest among the players or the number 78 is the tallest or rank 78th in performance among all players. No, it's not quantitative but categorical.

x x-x̅ (x-x̅)²

38 14.2 201.64

37 13.2 174.24

35 11.2 125.44

29 5.2 27.04

20 -3.8 14.44

19 -4.8 23.04

17 -6.8 46.24

15 -8.8 77.44

14.7 -9.1 82.81

13.3 -10.5 110.25

-----------------------------------------

Σ 238 882.58

For mean (x̅):

x̅ = 23.8

n = 10

For variance:

s² = Σ(x-x̅)² / (n-1) = 882.58 / 9 ≈ 98.064

For standard deviation:

s = √s² ≈ 9.9064

Range (R):

R = max-min = 38 - 13.3 = 24.7

Again, both variance and standard deviation are measures of variability of the data. It tells you the degree of spread of the data. If you try to change the minimum and/or maximum and make it closer to the mean, then both variance and standard deviation are going to be smaller in value. The list of numbers above are considered to be quantitative data because there is a certain ranking can be made.