Course STA301: Statistics and Probability
Practice Questions
Lecture No 1 to 5
Multiple Choice Questions:
(Sample questions)
1. Statistics deals with:
a) Observations
b) Aggregates of facts
c) Individuals
d) Isolated items
2. A number of students in a class is an example of:
a) Finite Population
b) Infinite Population
c) Hypothetical Population
d) None of these
3. A component bar chart in which
a) Each bar is divided into two or more sections
b) The value of a common variable in the form of grouped bars
c) The horizontal or vertical bars of equal with and length proportional to the values
d) None of these
4. What is the value of class mark for the given class 20-25?
a) 24
b) 22.5
c) 22
d) 15
5. The extremely positive skewed curve is also known as::
a) Frequency curve
b) U-shaped curve
c) J-shaped curve
d) Reverse J-shaped curve
Numerical Questions
(Sample questions)
Q1: Differentiate between Qualitative and Quantitative Variables.
Q2: Differentiate between Primary data and Secondary data.
Q3: Define Multiple Bar Chart.
Q4: Arrange the data given below in an array and construct a frequency distribution, using a class interval of 13, number of classes is 5 and the smallest observation is 09. Indicate the class boundaries and class limits clearly.
62, 73, 85, 42, 68, 54, 38, 27, 32, 63, 68, 69, 75, 59, 52, 58, 36, 85, 88, 72, 52, 52, 63, 68, 29, 73, 29, 76, 29, 57, 46, 43, 28, 32, 09, 66, 72, 68, 42, 76
Q5:Draw a Histogram and a Frequency Polygon for the following distribution.
Daily wages (Rs.)
|
4 – 6
|
6 – 8
|
8 – 10
|
10 – 12
|
12 – 14
|
14 – 16
|
No. of employees
|
13
|
111
|
182
|
105
|
19
|
7
|
ANSWERS / SOLUTION
Course STA301: Statistics and Probability
Practice Questions
Lecture No 1 to 5
Multiple Choice Questions:
6. Statistics deals with:
e) Observations
f) Aggregates of facts***
g) Individuals
h) Isolated items
7. A number of students in a class is an example of:
e) Finite Population***
f) Infinite Population
g) Hypothetical Population
h) None of these
8. A component bar chart in which
e) Each bar is divided into two or more sections***
f) The value of a common variable in the form of grouped bars
g) The horizontal or vertical bars of equal with and length proportional to the values
h) None of these
9. What is the value of class mark for the given class 20-25?
e) 24
f) 22.5***
g) 22
h) 15
10. The extremely positive skewed curve is also known as::
e) Frequency curve
f) U-shaped curve
g) J-shaped curve
h) Reverse J-shaped curve***
Numerical Questions
Q1: Differentiate between Qualitative and Quantitative Variables.
A variable whose characteristics can be measured numerically is called Quantitative Variable for example age, weight, income or number of children.
A variable whose characteristics cannot be measured numerically is called Qualitative Variable for example gender, education, intelligence or eye-color.
Q2: Differentiate between Primary data and Secondary data.
Data that have been originally collected (raw data) and have not undergone any statistical treatment are called Primary data.
Data that have undergone any statistical treatment at least once i.e. the data have been collected, classified, tabulated or presented in some form for a certain purpose are called Secondary data.
Q3: Define Multiple Bar Chart.
A multiple bar chart consists of two or more characteristics corresponding to the values of the common variable in form of grouped bars, whose lengths are proportional to the values where each bar is shaded with different colors to show their identification.
Q4: Arrange the data given below in an array and construct a frequency distribution, using a class interval of 13, number of classes is 5 and the smallest observation is 09. Indicate the class boundaries and class limits clearly.
62, 73, 85, 42, 68, 54, 38, 27, 32, 63, 68, 69, 75, 59, 52, 58, 36, 85, 88, 72, 52, 52, 63, 68, 29, 73, 29, 76, 29, 57, 46, 43, 28, 32, 09, 66, 72, 68, 42, 76.
Solution:
Class Limits
|
Frequency
|
Class Boundaries
|
9 – 21
|
1
|
8.5 – 21.5
|
22 – 34
|
7
|
21.5 – 34.5
|
35 – 47
|
6
|
34.5 – 47.5
|
48 – 60
|
7
|
47.5 – 60.5
|
61 – 73
|
13
|
60.5 – 73.5
|
74 – 86
|
5
|
73.5 – 86.5
|
87 – 99
|
1
|
86.5 – 99.5
|
40
|
Q5:Draw a Histogram and a Frequency Polygon for the following distribution.
Daily wages (Rs.)
|
4 – 6
|
6 – 8
|
8 – 10
|
10 – 12
|
12 – 14
|
14 – 16
|
No. of employees
|
13
|
111
|
182
|
105
|
19
|
7
|
Solution:
Daily wages
|
No. of wages
|
Mid points
|
4 – 6
|
13
|
5
|
6 – 8
|
111
|
7
|
8 – 10
|
182
|
9
|
10 – 12
|
105
|
11
|
12 – 14
|
19
|
13
|
14 – 16
|
7
|
15
|
Histogram:
Frequency Polygon:
Download STA301 Question
Course STA301: Statistics and Probability
Practice Questions
Lecture No 6 to 10
MCQs
1. The
value that occurs most often in a set of data is called the:
a)
Mean
b)
Mode
c)
Geometric mean
d)
Harmonic mean
2. Find the mean of the following sample of
distances of stars from the earth:
18.2, 56.9, 24.6, 13.5
3. Which
of the following is a true statement about the median?
a)
It is always one
of the data values.
b)
It is influenced
by extreme values.
c)
Fifty percent of
the observations are larger than the median.
d)
It is the middle
value of the data values.
4. The G.M of 2, 4 and 8 is
a)
3.67
b)
4
c)
3.43
d)
5
5. One of the main disadvantages of the range
is:
a)
It does not use
all the observations in its calculations
b)
It cannot be
influenced by an extreme value
c)
It does not
involve negative values
d)
It deals with
open ended classes
Question
1:
Find the mode, for the distribution of examination
marks given below:
Marks
|
30-39
|
40-49
|
50-59
|
60-69
|
70-79
|
80-89
|
90-99
|
Number of Students
|
8
|
87
|
190
|
304
|
211
|
85
|
20
|
Question
2:
Find the mean weight of 120 students at the Punjab
University from the frequency distribution:
Weight (pounds)
|
Number of students
|
110-119
|
1
|
120-129
|
4
|
130-139
|
17
|
140-149
|
28
|
150-159
|
25
|
160-169
|
18
|
170-179
|
13
|
180-189
|
6
|
190-199
|
5
|
200-209
|
2
|
210-219
|
1
|
Question
3
If mode =25 and median = 30, then find approximate
value of mean
Question
4:
Find the harmonic mean from the following frequency
distribution of weights:
Weights (grams)
|
65-84
|
85-104
|
105-124
|
125-144
|
145-164
|
165-184
|
185-204
|
f
|
9
|
10
|
17
|
10
|
5
|
4
|
5
|
Question
5
Find semi-inter quartile range, if Q1=
1423.36 and Q3 = 167.83
Practice Question with SOLUTION
Course STA301: Statistics and Probability
Lecture No 6 to 10
2. The
value that occurs most often in a set of data is called the:
a)
Mean
b)
Mode
c)
Geometric mean
d)
Harmonic mean
Answer key: b)
2. Find the mean of the following sample of
distances of stars from the earth:
18.2, 56.9, 24.6, 13.5
Answer
Key= a)
3. Which
of the following is a true statement about the median?
a) It
is always one of the data values.
b) It
is influenced by extreme values.
c) Fifty
percent of the observations are larger than the median.
d) It
is the middle value of the data values.
Answer Key= d)
4. The G.M of 2, 4 and 8 is
a)
3.67
b)
4
c)
3.43
d)
5
Answer Key= b)
5. One of the main disadvantages of the range
is:
a)
It does not use
all the observations in its calculations
b)
It cannot be
influenced by an extreme value
c)
It does not
involve negative values
d)
It deals with
open ended classes
Answer key = a)
Question
1:
Find the mode, for the distribution of examination
marks given below:
Marks
|
30-39
|
40-49
|
50-59
|
60-69
|
70-79
|
80-89
|
90-99
|
Number of Students
|
8
|
87
|
190
|
304
|
211
|
85
|
20
|
Solution:
The class that carries the highest frequency is
59.5-69.5 which the modal class is thus
Question
2:
Find the mean weight of 120 students at the Punjab
University from the frequency distribution:
Weight (pounds)
|
Number of students
|
110-119
|
1
|
120-129
|
4
|
130-139
|
17
|
140-149
|
28
|
150-159
|
25
|
160-169
|
18
|
170-179
|
13
|
180-189
|
6
|
190-199
|
5
|
200-209
|
2
|
210-219
|
1
|
Solution:
Weight (pounds)
|
Number of students(f)
|
Class Mark (X)
|
fX
|
110-119
|
1
|
114.5
|
114.5
|
120-129
|
4
|
124.5
|
498.0
|
130-139
|
17
|
134.5
|
2286.5
|
140-149
|
28
|
144.5
|
4046.0
|
150-159
|
25
|
154.5
|
3862.5
|
160-169
|
18
|
164.5
|
2961.0
|
170-179
|
13
|
174.5
|
2268.5
|
180-189
|
6
|
184.5
|
1107.0
|
190-199
|
5
|
194.5
|
972.5
|
200-209
|
2
|
204.5
|
409.0
|
210-219
|
1
|
214.5
|
214.5
|
n=∑f=120
|
∑fX=18740
|
Question
3
If mode =25 and median = 30, then find approximate
value of mean
Solution:
Mode= 3 Median-2 Mean
25=3(30)-2(Mean)
25=90-2(Mean)
2(Mean) =90-25
2(Mean) =65
Mean=32.5
Question
4:
Find the harmonic mean from the following frequency
distribution of weights:
Weights (grams)
|
65-84
|
85-104
|
105-124
|
125-144
|
145-164
|
165-184
|
185-204
|
f
|
9
|
10
|
17
|
10
|
5
|
4
|
5
|
Solution:
We calculate the harmonic mean as below
Weights
(grams)
|
f
|
X
|
f(1/X)
|
65-84
|
9
|
74.5
|
0.12081
|
85-104
|
10
|
94.5
|
0.10582
|
105-124
|
17
|
114.5
|
0.14847
|
125-144
|
10
|
134.5
|
0.07435
|
145-164
|
5
|
154.5
|
0.03236
|
165-184
|
4
|
174.5
|
0.02292
|
185-204
|
5
|
194.5
|
0.02571
|
60
|
0.53044
|
Hence H=
Question
5
Find semi-inter quartile range, if Q1=
1423.36 and Q3 = 167.83
Solution:
No comments:
Post a Comment