# Question Bank for Statistics

Topic : A) Descriptive Statistics :

A1. A bank recorded the age at which an individual first opened a Savings Bank Account and were as follows:

42

44

52

32

23

25

34

33

37

18

19

18

14

16

18

18

23

21

18

23

24

24

26

28

32

43

33

34

19

23

22

21

18

19

18

22

25

24

54

20

21

17

22

24

25

22

23

5

8

29

18

16

17

15

19

21

32

33

34

35

36

37

23

24

25

21

22

33

33

43

27

28

29

30

31

33

17

25

23

25

33

23

25

26

27

28

18

19

20

21

16

16

17

19

21

22

20

21

22

23

a) Draw a frequency distribution for the above data.

b) Draw a suitable chart to indicate the age at which individuals open a Savings Account. c) What type of distribution does the data reveal.

d) Is there any data which you would not like to consider for exhibiting the data e) Calculate the different measures of descriptive statistics and indicate the measure of central tendency which would be the most appropriate.

A2. The following firms have submitted their request for availing loan for their project and these are as follows: Firms

a

b

c

d

e

f

g

h

Loan amount ( Rs. In lakhs)

5.6

2.5

8.6

4.6

3.75

1

2.5

20.5

Purpose

Buy tractor

Purchase of car

Buy drilling machine

marriage

Purchase of car

Flat renovation

Purchase of car

Plot of land

Period for which loan is required( months)

18

10

24

18

12

6

12

120

a) Indicate the scales in which each of the variable has been measured. b) What is the modal purpose for which loan is availed by the firm. c) What is the average loan amount given by the bank.

d) Is there any type of loan for which this bank is specializing.

A3. A manager in a bank is evaluating the performance of his Relationship Managers and has collected the following information : Employee

RM1

RM2

RM3

RM4

Number of sales calls a month

100

120

60

90

Amount of deposits obtained(in lakhs)

250

200

150

195

Target Potential of deposits

300

280

250

240

Number of customers allotted

50

75

40

70

What are different criteria the manager can use to understand the performance of his four relationship managers in the bank.

A4. Among 50 clerical staff in an office the number of absenteeism recorded each day for the next 30 days are as follows: 3

0

1

4

6

2

5

4

7

3

8

0

0

1

3

4

6

7

8

2

10

4

6

12

5

6

8

9

1

12

a) Find the average, standard deviation, for the amount of absenteeism for the month. b) Present the data in the form of frequency distribution.

c) Describe the shape of the distribution.

A5. A bank has given the following average interest rates during the last 3 years. 2009-10 -- 8% , 2010-11 -- 6.75%, 2011-12 – 8.5%, What is the average rate of interest that the bank has given in the past three years.

A6. The following are the data for the annual profits over the past 30 years for a small business ( in thousand’s of Rs. ) 15

17

18

19

20

20

20

21

23

24

24

24

24

25

34

32

28

29

40

41

32

22

32

33

35

36

29

27

36

40

a) Construct a stem and leaf plot .

b) find the mean and median

A7. Look into the internet and obtain data for coffee production among the different countries. Use a suitable chart to indicate the production of coffee from India.

A8. The weight (kgs)of new born babies in a city hospital have been taken at random and found as follows: 3.2

2.8

2.5

4.4

4.2

3.8

3.9

2.85

4.1

5.5

4.3

4.5

5.3

2.9

3.1

3.0

3.1

3.6

3.7

3.8

5.0

5.2

4.6

4.3

4.7

3.8

3.9

3.1

3.2

3.2

It is considered that babies born with a weight of less than 3Kg are considered underweight and needs special care. Based on the above data calculate the following

a) Mean weight of babies and proportion of babies who are underweight. b) Measure the dispersion, skewness and kurtosis for the weight of the babies c) Plot the weight as a stem and leaf plot...

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