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Assignment No.1 (Course STA301)Fall 2011 (Total Marks 30)

DeadlineYour Assignment must be uploaded/ submitted before or on

STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIRASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENTAFTER DUE DATE WILL BE ACCEPTED VIA E.MAIL).

Rules for MarkingIt should be clear that your Assignment will not get any creditIF:

The Assignment submitted, via email, after due date.

The submitted Assignment is not found as MS Worddocument file.

There will be unnecessary, extra or irrelevant material.

The Statistical notations/symbols are not well-written i.e.,without using MathType software.

The Assignment will be copied from handouts, internet orfrom any other students file. Copied material (fromhandouts, any book or by any website) will be awardedZERO MARKS. It is PLAGIARISM and an Academic Crime.

The medium of the course is English. Assignment in Urduor Roman languages will not be accepted.

Assignment means Comprehensive yet precise accuratedetails about the given topic quoting different sources

(books/articles/websites etc.). Do not rely only onhandouts. You can take data/information from differentauthentic sources (like books, magazines, website etc) BUTexpress/organize all the collected material in YOUR OWNWORDS. Only then you will get good marks.

Objective(s) of this Assignment:

The assignment is being uploaded to strengthen thestudents BASIC concepts about statistics.

Practice for arranging and displaying already collecteddata into an organized form, using given statisticalmethod.

Make students able to understand the concept ofmeasures of central tendency.

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Assignment.1 (Lessons 1-10)

Question 1: Marks: 5+5=10i) From the table given below, Find

(a) Class boundaries

(b) How many men fall above the age of 50?(c) How many men fall between the age group of 60 and 69?

Age Group (Men) f

20-29 5

30-39 4

40-49 5

50-59 8

60-69 1270-79 16

Total 50

Answer:(a)

Age Group (Men) f C.B

20-29 5 19.5-29.5

30-39 4 29.5-39.5

40-49 5 39.5-49.550-59 8 49.5-59.5

60-69 12 59.5-69.5

70-79 16 69.5-79.5

Total 50

(b) Men fall above the age of 50= 8+12+16 = 36(c) Men fall between the age group of 60 and 69= 12

(ii) Write down the following figure in the form of frequency table and also find the

relative frequency.

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0

1

2

3

4

5

6

7

8

3-5 6-9 10-13 14-16 17-19

Ages of Students

N

o.ofStud

Answer:

.

Ages Frequency Relative

frequency

3-56-910-13

14-16

17-19

257

3

2

2/195/197/19

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Question 2: Marks: 5+5=10

(i)Calculate the mode from the following continuous distribution.

Height Number (f)

57.5-60.0 6

60.0-62.5 2662.5-65.0 190

65.0-67.5 281

67.5-70.0 412

70.0-72.5 127

72.5-75.0 38

Total 1080

Answer:From the table we locate modal class frequency as 412 and hence we get

1 2412, 281, 127, 67.5, 2.5

mf f f l h= = = = =

( )

( ) ( )

1

1 2

( )

412 28167.5 2.5

412 281 412 127

13167.5 2.5

131 285

68.29

m

m m

f fX l h

f f f f

= +

+

= +

+

= + +

=

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(ii). Use the stem and leaf plot to answer these questions.

Statistics Test Scores

Stem Leaf

6 1 1 4 6 7 8

7 2 3 5 7 9

8 1 3 5 6 6 7 7 8 9

9 0 0 3 4 6 8 9 9

10 0 0

a) What is the best test score?

b) How many students took the test?

c) How many students scored 90?

d) What is the lowest score?

e) Find the difference between the high and low scores.

Answer:

a) The best test score =100

b) The students took the test = 30

c) The students scored 90 = 2

d) The lowest score= 61

e) The difference between the high and low scores = 39

Question 3: Marks: 3+3+4=10

(i) Find the median for the following discrete frequency distribution.

Number of pupils per class Number of Classes

20 1

21 0

22 1

23 324 6

25 9

26 8

27 10

28 7

Total 45

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Answer:

23rd value in Cumulative frequency is against 26

Hence the median is 26.

(ii) Calculate the weighted mean from the following data

Item Expenditure Weights

Food 290 7.5

Rent 54 2.0

Clothing 98 1.5

Fuel and light 75 1.0

Other items 75 0.5

Answer:

We calculate the weighted mean as below:

Item Expenditure Weights xwFood 290 7.5 2175.0

Rent 54 2.0 108.0

Clothing 98 1.5 147.0

Fuel and light 75 1.0 75.0

Other items 75 0.5 37.5

Total 12.5 2542.5

2542.5.203.4

12.5w

WXX Rs

W= = =

Number of pupils per class Number of Classes Cumulative frequency

20 1 1

21 0 1

22 1 2

23 3 5

24 6 11

25 9 20

26 8 28

27 10 38

28 7 45

Total 45

1

1

( )2

45 1( )

2

23

n

i

rd

f

thvalue

thvalue

value

=

+

=

+=

=

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(iii) A man gets a rise of 10% in salary at the end of his first year of service and further of

20 % and 25 % at the end of the second and third year respectively. The rise in each case is

calculated on his salary at the beginning of the year. To what annual percentage increase in

this equivalent?

Sol

Suppose the initial salary of the man = 100

At the end of Increment Salary (Y)

First year 10% 110

Second year 20% 120

Third year 25% 125

3. 110 120 125 118.16G M = =

Annual percent increase = 118.16-100 = 18.16%