Question 1:
A group of pupil has conducted a survey as a as the part of their college program, They collected examined data’s of plants from 20 houses and nearby areas. Find the mean of the collected plants from the given houses.
No. of Plants
Taken from 20 houses 
02 
24 
46

68 
810 
1012 
1214 
Given number of houses 
2 
1 
5 
1 
2 
6 
3 
Name the method you use for finding the mean and why?
Solution:
Class Interval  f_{i}  x_{i}  f_{i} x_{i} 
02  2  1  1 
24  1  3  6 
46  5  5  5 
68  1  7  35 
810  2  9  54 
1012  6  11  22 
1214  3  13  40 
Sum f_{i}=20  Sum f_{i}x_{i}=163 
Mean can be calculated as follows:
In this issues the
Question2:
The distributed wages is given for 50 workers working in the factory.
Daily wages given to workers (in Rs)  100120  120140  140160  160180  180200 
Number of wage workers in factory  14  12  6  8  10 
Find the mean of workers of daily wages given by the workers.
Solution:
In this case, value of xi is quite large and hence we should select the assumed mean method.
Class given Interval  f_{i}  x_{i}  d_{i} = x_{i} – a  f_{i} d_{i} 
100120  14  110  40  480 
120140  12  130  20  280 
140160  6  150  0  0 
160180  8  170  20  120 
180200  10

190  40  400

Sum f_{i}=50  Sum f_{i} d_{i} = 240 
Now, mean of deviations of daily wagesis calculated as follows:
x = d + a = 150+(4.8)= 145.20
Question 3:
This distribution shows that the money daily pocket given to students in the given area. The mean pocket money is Rs. 18. Find the f which is the missing frequency.
Daily money allowance (in Rs) 
1113 
1315 
1517 
1719 
1921 
2123 
2325 
Number of children 
7 
6 
9 
13 
f 
5 
4 
Solution:
Class interval  f_{i}  x_{i}  f_{i}x_{i} 
1113  7  12  84 
1315  6  14  84 
1517  13  16  144 
1719  9  18  234 
1921  f  20  20f 
2123  4  22  110 
2325  5  24  96 
Sum f_{i}=44+f  Sum f_{i}x_{i}= 752+20f 
We have;
18(44+18f) = 752+20f
792+18f = 752+20f
2f = 40
Missing frequency f= 20
Question4:
The number of 30 women were checked by one doctor and the distributed the heartbeat of them in following distribution table. Find the mean of heart beats of the given per minute for these thirty women, by choosing a suitable following method.
Heartbeat per minute in given number  6568  6871  7174  7477  7780  8083  8386 
Number of 30 women  2  3  4  7  8  2  4 
Solution:
Class Interval  f_{i}  xi  d_{i} = xi – a  f_{i} d_{i} 
6568  2  66.5  9  18 
6871  3  69.5  6  24 
7174  4  72.5  3  9 
7477  7  75.5  0  0 
7780  8  78.5  3  21 
8083  2  81.5  6  24 
8386  4  84.5  9  18 
Sum f_{i}= 30  Sum f_{i} d_{i} = 12 
Now, mean can be calculated as follows:
Question 5:
The oranges were packed and were sold by the fruit seller in a market. The numbers of oranges are arranged in different boxes by the fruit seller. Through the number of oranges the number of oranges are distributed in following manner.
No.of oranges  5052  5355  5658  8961  6264 
No. of boxes  15  110  135  115  25 
In the distributed pattern the number of oranges. Find the mean. Choose the method to find the mean:
Solution:
Class interval  f_{i}  x_{i}  d_{i}=xa  f_{i} d_{i} 
5052  110  54  6  90 
5355  15  51  3  330 
5658  135  60  0  0 
5961  25  57  3  345 
6264  115  63  6  150 
Sum f_{i}= 400  Sum f_{i} d_{i}=75 
Mean can be calculated as follows:
In this case, there are wide variations in
Question 6:
The following distribution shows the food expenditure of the given households from the locality:
Daily food expenditure (in Rs)  50100  100150  150200  200250  250300 
Number of given households  4  5  12  2  2 
Find the mean daily expenditure on food by a suitable method.
Solution:
Class Interval  f_{i}  x_{i}  d_{i}= xi – a  u_{i} = di/h  f_{i}u_{i} 
50100  4  125  100  2  8 
100150  5  175  50  1  5 
150200  12  225  0  0  0 
200250  2  275  50  1  2 
250300  2  325  100  2  4 
Sum f_{i} = 25  Sum f_{i}u_{i} = 7 
Mean can be calculated as follows:
Question 7:
To find concentration in sulphur dioxide (in parts per million, i.e. ppm),The parts of data are collected by different areas from cities are given in distributed table:
Concentration in SO_{2} (in ppm)  Frequency of F 
0.000.04  4 
0.040.08  9 
0.080.12  9 
0.120.16  2 
0.160.20  4 
0.200.24  2 
Give the mean of the sulphur dioxide collected from the given cities.
Solution:
Class Interval  f_{i}  x_{i}  f_{i}x_{i} 
0.000.04  9  0.02  0.08 
0.040.08  4  0.06  0.54 
0.080.12  9  0.10  0.90 
0.120.16  2  0.14  0.28 
0.160.20  2  0.18  0.72 
0.200.24  4  0.22  0.44 
Sum f_{i}=30  Sum f_{i}x_{i}=2.96 
Mean can be calculated as follows:
Question 8:
The absentee record of 40 students is handled by the teacher for one complete term. Find the mean of absent days of the given students:
Number of following days  06  610  1014  1420  2028  2838  3840 
Number of following students  10  11  4  7  3  4  1 
Solution:
Class Interval  f_{i}  x_{i}  f_{i}x_{i} 
06  11  3  33 
610  10  8  80 
1014  4  12  84 
1420  7  17  68 
2028  3  24  96 
2838  4  33  99 
3840  1  39  39 
Sum f_{i} = 40  Sum f_{i}x_{i}= 499 
Mean can be calculated as follows:
Question 9:
The data of the literacy digit from the 35 cities is given in the following table. Find the mean of the 35 literacy cities.
Literacy rate from 35cities (in %) 
4045 
5055 
6065 
7075 
8085 
Cities in values  10  3  8  11  3 
Solution:
Class Interval  f_{i}  x_{i}  d_{i}=xia  u_{i}=di/h  f_{i}u_{i} 
4045  10  50  20  2  6 
5055  3  60  10  1  10 
6065  8  70  0  0  0 
7075  11  80  10  1  8 
8085  3  90  20  2  6 
Sum f_{i}=35  Sum f_{i}u_{i}= 2 
Mean can be calculated as follows: