Question

For the following sample data, answer the following:
Remember you can copy and "paste special" the table into the Excel sheet.

73

24

74

65

96

46

75

20

36

77

95

5

49

19

What is ¯xx¯ ?  
What is the median?   
What is the standard deviation?  
What is the Q₁?
What is the range?

Answer 1

Write data in ascending order

3 , 5 , 19 , 20 , 24 , 36 , 46 , 49 , 65 , 74 , 75 , 77 , 95, 96

= X / n

= 684 / 14

= 48.86

Median = ( n + 1) / 2 th observation

= ( 14 + 1) / 2

= 7.5 th observation

= 47.5

Standard deviation = sqrt [ X² - n ² / n -1 ]

= sqrt [ (46680 - 14 * 48.86² ) / 13 ]

= 31.94

Q1 = ( n + 1) / 4 th observation

= ( 14 +1 )/ 4

= 3.75 th observation

= 19.75

Range = Maximum value - Minimum value

= 96 - 3

= 93