37.
Find the mean by step-deviation Method.
1000-1500 1500-2000 2000-2500 2500-3000 3000-3500 3500-4000 4000-4500 4500-5000
Expenditure
(In)
Frequency
24
33
28
30
22
16
7
Answers
Answer:
Expenditure
(in rupees) x
i
Frequency
(f
i
) f
i
x
i
1000-1500 1250 24 30000
1500-2000 1750 40 70000
2000-2500 2250 33 74250
2500-3000 2750 28 77000
3000-3500 3250 30 97500
3500-4000 3750 22 82500
4000-4500 4250 16 68000
4500-5000 4750 7 33250
Σf
i
=200 Σf
i
x
i
=532500
Mean=
Σf
i
Σf
i
x
i
=
200
532500
=2662.5
As frequency is maximum for the class 1500-2000, modal class is 1500−2000.
Mode=l+
2f
1
−(f
0
+f
2
)
f
1
−f
0
×h
where,
l = lower limit of modal class =1500
f
1
= frequency of modal class = 40
f
0
= frequency of class preceding the modal class = 24
f
2
= frequency of class succeding the modal class = 33
h = higher limit - lower limit =2000−1500=500
Mode=1500+
2×40−(24+33)
40−24
×500
⇒mode=1500+
23
16
×500=1500+347.83=1847.83
Hence, the mean and modal monthly expenditure of the families are 2662.5 and 1847.83 respectively.