Question

# Class Limits (Age in years) , Frequency 0-9 ,1 10-19, 7 20-29, 12 30-39 ,12 40-49,...

Class Limits (Age in years) , Frequency

0-9 ,1

10-19, 7

20-29, 12

30-39 ,12

40-49, 23

50-59, 23

60-69 ,32

70-79 ,9

80-89 ,4

90-99, 1

Find the mean, calculate sample variance and sample standard deviation,

Solution:

 Group Midpoint X Frequency f f*x x2 f*(x2) 0-9 4.5 1 4.5 20.25 20.25 10 -19 14.5 7 101.5 210.25 1471.75 20-29 24.5 12 294 600.25 7203 30-39 34.5 12 414 1190.25 14283 40-49 44.5 23 1023.5 1980.25 45545.75 50-59 54.5 23 1253.5 2970.25 68315.75 60-69 64.5 32 2064 4160.25 133128 70-79 74.5 9 670.5 5550.25 49952.25 80-89 84.5 4 338 7140.25 28561 90-99 94.5 1 94.5 8930.25 8930.25 SUM 495 124 6258 32752.5 357411

1)

= = 6258/124 = 50.4677419355

Mean = 50.4677419355

2)

Variance =

= [357411/124] - [50.46774193552]

= 335.353798125

Variance = 335.353798125

3)

Standard deviation = positive root of variance = 18.3126676955

Standard deviation = 18.3126676955

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