Statistics Most important questions

CHAPTER – 14
STATISTICS
MEAN OF GROUPED DATA
Direct method

Mean, x 
 fi x i
 fi
Assume mean method or Short-cut method

Mean, x  A 
 fi d i where d  x  A
i i
 fi
Step Deviation method (This method deleted but student can use this method also)

Mean, x  A 
 fiu i  h where u  xi  A
 fi h

IMPORTANT QUESTIONS
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy
rate.
Literacy rate (in %) 45 – 55 55 – 65 65 – 75 75 – 85 85 – 95
Number of cities 3 10 11 8 3
Solution:
Literacy rate Number of Class mark x A fu
(in %) Cities ‘f’ ‘x’ u 
h
45 – 55 3 50 –2 –6
55 – 65 10 60 –1 –10
65 – 75 11 70 0 0
75 – 85 8 80 1 8
85 – 95 3 90 2 6
Total 35 –2

Here, fu  2,  f  35 , A = 70, h = 10
Mean, x  A    h =  x  70   10  70 
fu 2 20 4
 70   70  0.57  x  69.43
f 35 35 7

Questions for Practice
1. Find the mean of the following data:
Class Interval 10 – 25 25 – 40 40 – 55 55 – 70 70 – 85 85 – 100
Frequency 2 3 7 6 6 6
2. Find the mean percentage of female teachers of the following data:
Percentage of female 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 65 – 75 75 – 85
teachers
Number of States/U.T 6 11 7 4 4 2 1
3. A survey was conducted by a group of students as a part of their environment awareness
programme, in which they collected the following data regarding the number of plants in 20
houses in a locality. Find the mean number of plants per house.
Number of plants 0 – 2 2 – 4 4 – 6 6 – 8 8 – 10 10 – 12 12 – 14
Number of houses 1 2 1 5 6 2 3

, 4. Find the mean daily wages of the workers of the factory by using an appropriate method for the
following data:
Daily wages (in Rs) 100 – 120 120 – 140 140 – 160 160 – 180 180 – 200
Number of workers 12 14 8 6 10
5. Find the mean number of mangoes kept in a packing box for the following data:
Number of mangoes 50 – 52 53 – 55 56 – 58 59 – 61 62 – 64
Number of boxes 15 110 135 115 25
6. Find the mean daily expenditure on food for the following data:
Daily expenditure (in Rs.) 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350
Number of households 4 5 12 2 2


MODE OF GROUPED DATA
 f1  f 0 
Mode  l    h
 2 f1  f 0  f 2 
where l = lower limit of the modal class,
h = size of the class interval (assuming all class sizes to be equal),
f1 = frequency of the modal class,
f0 = frequency of the class preceding the modal class,
f2 = frequency of the class succeeding the modal class.

IMPORTANT QUESTIONS

Find the mean, mode and median for the following frequency distribution.
Class 0-10 10-20 20-30 30-40 40-50 Total
Frequency 8 16 36 34 6 100
Solution:
Here, highest frequency is 36 which belongs to class 20 – 30. So, modal class is 20 – 30,
l = 20, f0 = 16, f1 = 36, f2 = 34, h = 10
 f1  f 0 
We know that Mode  l    h
 2 f1  f 0  f 2 
36  16
 Mode  20   10
2(36)  16  34
20 200
 Mode  20   10  20   20  9.09  29.09
72  50 22

Questions for Practice
1. The frequency distribution table of agriculture holdings in a village is given below:
Area of land(in ha) 1-3 3-5 5-7 79 9-11 11-13
No. of families 20 45 80 55 40 12
Find the modal agriculture holdings of the village.
2. Find the mode age of the patients from the following distribution :
Age(in years) 6-15 16-25 26-35 36-45 46-55 56-65
No. of patients 6 11 21 23 14 5
3. Find the mode of the following frequency distribution:
Class 25-30 30-35 35-40 40-45 45-50 50-55
Frequency 25 34 50 42 38 14