Question no.
1
Classify the following as qualitative or quantitative variables.
i. Weight measurements of students
ii. Race of the people of a country
iii. Likings or dislikings of 1000 persons for a certain product
iv. Expenditure Government servants of a city
v. Color of eyes of 1000 persons
Solution:
i. Quantitative
ii. Qualitative
iii. Qualitative
iv. Quantitative
v. Qualitative
Question no.2
Define quantitative and qualitative variables.
Solution:
Quantitative variable:
A variable is called a quantitative variable when a characteristic can be expressed
numerically such as age, weight, income or number of children.
Qualitative variable:
If the characteristic is non-numerical such as education, sex, eye-color, quality,
intelligence, poverty, satisfaction, etc. the variable is referred to as a qualitative variable.
A qualitative characteristic is also called an attribute.
Question no.3
Name five fields where statistics can contribute?
Business and industry
Health and medicine
Natural and social sciences
Natural resources
Education, Government media and law
Question no.4
Find the Cumulative frequencies for the frequency distribution given below:
Out put in
50 - 59 60 -69 70 - 79 80 - 89 90 - 99 100 - 109
tons
f 3 11 19 28 20 15
Cumulative
Out put in tons f Frequency
(F)
50-59 3 3
60-69 11 14
70-79 19 33
80-89 28 61
90-99 20 81
100-109 15 96
Total 96 ….
Question no.5
If frequency =15 and frequency density=0.3, then find the class width.
Solution:
Frequency density= frequency/class width
Calss width=frequency/frequency density=15/0.3=50
Question no.6
Calculate the frequency density when class width =6 and frequency=24
Solution:
Frequency density= frequency/class width
=24/6=4
Question no.7
Find the frequency density for the distribution given below:
Class
50 - 59 60 -69 70 - 79 80 - 89 90 - 99 100 - 109
intervals
f 4 11 18 28 22 15
Solution:
Class intervals Class width f Frequency density
(F)
50-59 9 4 4 /9
60-69 9 11 11/9
70-79 9 18 18/9
80-89 9 28 28/9
90-99 9 22 22/9
100-109 9 15 15/9
Question no.8
Find the Relative frequencies for the frequency distribution given below:
Out put in
50 - 59 60 -69 70 - 79 80 - 89 90 - 99 100 - 109
tons
f 15 12 10 28 25 10
Relative
Out put in tons f Frequency
(F)
50-59 15 15/100=0.15
60-69 12 12/100=0.12
70-79 10 10/100=0.1
80-89 28 28/100=0.28
90-99 25 25/100=0.25
100-109 10 10/100=0.1
Total 100 ….
Question no.9
Following is the group frequency distribution of 94 students which shows their test result
in a class. Find the arithmetic mean.
Class Interval No. Of Students
10-20 5
20-30 16
30-40 12
40-50 25
50-60 17
60-70 8
70-80 6
Class Interval f1 Class X1 fxi
Boundry
10-20 5 9.5-20.5 (9.5+20.5)/2=15 75
20-30 16 19.5-30.5 25 400
30-40 12 29.5-40.5 35 420
40-50 25 39.5-50.5 45 1125
50-60 17 49.5-60.5 55 935
60-70 8 59.5-70.5 65 520
70-80 6 69.5-80.5 75 450
Arithmetic mean = Sum fxi/sumf = 3925/89= 44.10
Note: Class boundry column is not necessary. If student directly calculate Xi by
taking average of class interval then it is also correct.
Question no.10
Complete the following table by finding angles for the pie chart:
Medium of
Frequency Angle
Institution
Urdu 436
English 764
1200
Medium of
Frequency Angle
Institution
Urdu 436 130.8
English 764 229.2
1200 360o
Question no.11
For grouped data the median is given by:
h n
M e Lo F
fo 2
in this formula what these things stands for?
Lo , f o , h, F
L0 = Lower class boundary of the median class
h = Width of the median class
f0 = Frequency of the median class
F = Cumulative frequency of the pre-median class
Question no.12
The data of profit (in Rs lakh) earned by 60 companies is given below:
Profits Below 10 10-20 20-30 30- 40 40-50 50 and over
No. of companies 5 18 22 16 7 2
Cumulative 5 23 45 61 68 70
frequency
Find Median for the above data.
Median= size of n/2 th observation which lies in the class 20-30
h n
Q2 l C
f 2
10
Q2 20 35 23
22
Q2 20 5.45
25.45 lakh
Question no.13
Consider the data set: 67 25 42 57 38 49 36 29 61 31 71 53 73
84 87
Find the 50th percentile point.
First arrange the data in ascending order
25 29 31 36 38 42 49 53 57 61 67 71 73 84 87
Location of 50th Percentile is (15+1) (50/100) = 8th value = 53
Question no.14
Give a five number summary of the data.
15, 17, 18, 19, 35, 25, 14, 45, 37, 51, 42
Re arrange data in ascending order
14, 15, 17, 18, 19, 25, 35, 37, 42, 45, 51
Minimum = 14
First Quartile = ( 11+1)(25/100) = 3rd position = 17
Median = 25
Third Quartile = (11 + 1) ( 75/100) = 9th position = 42
Maximum = 51
