3.   The following distribution shows the daily pocket allowance of children of a locality.
The mean pocket allowance is Rs 18. Find the missing frequency f.



Daily pocket allowance (in ₹)
Number of children
11 - 13
7
13-15
6
15-17
9
17-19
13
19-21
$f$
21-23
5
23-25
4



Solution:
Let use direct method .

Daily pocket allowance (in ₹)
Number of children($f_i$)
Midpoint($x_i$)
$f_ix_i$
11 - 13
7
12
84
13-15
6
14
84
15-17
9
16
144
17-19
13
18
234
19-21
$f$
20
20$f$
21-23
5
22
110
23-25
4
24
96
Total
44 + $f$
752+20$f$

Since mean is give as $x̄$ = ${∑f_ix_i}/{∑f_i}$
Therefore  $18$= $(752+20f)/(44+f)$
           $792+18f=752+20f$
		   $20f-18f=792-752$
		   $2f=40$
		   $f=20$
		   
	Answer: $f$= 20
	

4.   Thirty women were examined in a hospital by a doctor and the number of heartbeats 
per minute were recorded and summarised as follows. Find the mean heartbeats per minute
 for these women, choosing a suitable method.	
 
 
 
 
Number of heartbeats per minute
Number of women 
 
65-68
2
 
68-71
4
 
71-74
3
 
74-77
8
 
77-80
7
 
80-83
4
 
83-86
2
 
 
 Solution:
  
 
 
Number of heartbeats per minute
Number of women ($f_i$)
Midpoint($x_i$)
$f_ix_i$
 
65-68
2
66.5
133
 
68-71
4
69.5
278
 
71-74
3
72.5
217.5
 
74-77
8
75.5
604
 
77-80
7
78.5
549.5
 
80-83
4
81.5
326
 
83-86
2
84.5
169
 
Total
30
2277
 

Since mean is give as $x̄$ = ${∑f_ix_i}/{∑f_i}$
                                = $2277/30$
                                = $75.9$
								
Answer: Mean heartbeart per minute = $75.9$