Question

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,

Answer 1

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