Question

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? 99 53 74 58 1 98 10 19 7 48 61

Answer 1

SOLUTION:

From given data,

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? 99 53 74 58 1 98 10 19 7 48 61

99

53

74

58

1

98

10

19

7

48

61

Find The​ range

Let us write the data in increasing order,

1

7

10

19

48

53

58

61

74

98

99

Formula for range is

Range = Maximum value - Minimum value

Where,

Maximum value = 99

Minimum value = 1

Then ,

Range = 99 - 1 = 98

Range = 98

Find the​ variance:

= 99 +53+ 74 +58+ 1+ 98+ 10 +19 +7 +48+ 61 = 528

Mean = = / = 528 / 11 = 48

Variance = S² = (-)² / (-1)

(-)² = (99-48)^2 +(53-48)^2+ (74-48)^2 +(58-48)^2+( 1-48)^2+( 98-48)^2+ (10-48)^2 +(19-48)^2 +(7-48)^2 +(48-48)^2+ (61-48)^2 = 12246

S² = 12246/ (11-1)

S² = 12246/ 10 =1224.6

Variance =S² = 1224.6

Find the​ standard deviation:

standard deviation = S = sqrt(S²) = sqrt(1224.6) = 34.99