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MID-TERM QUESTION PAPER
QUANTITATIVE TECHNIQUES
TIME ALLOWED
: 2 hours
Maximum Marks: 50
Attempt all questions :
(It is an open book test. Please show complete working notes)
Q-1) Construct a sub-divided bar chart for the 3 types of expenditures in dollars of a
family of four for the years 2002, 2003, 2004 and 2005 as given below:
Year
2002
2003
2004
2005
10 marks
Expenditure
Food
3000
3500
4000
5000
Education
2000
3000
3500
5000
Other
3000
4000
5000
6000
Total
8000
10500
12500
16000
The sub-divided bar chart would be as follows:
OR
Class Interval
Frequency
Cumulative Frequency
Less than
Construct “Less than ogive” and “More than ogive”
Cumulative Frequency
More than
10 marks
15 Upton 25
25 “ 35
35 “ 45
45 “ 55
55 “ 65
65 “ 75
5
3
7
5
3
7
5
8
15
20
23
30
30
25
22
15
10
7
OR
Write the difference between Bar diagram and Histogram
Q-2) Calculate the Karl Pearson’s Coefficient of Skewness for the following
Class Interval
f
5-10
10-15
15-20
20-25
25-30
30-35
35-40
5
10
15
20
15
10
5
15 marks
OR
Calculate the i) Quartile Deviation iii) Coefficient of Skewness
Class Interval
5-10
10-15
15-20
20-25
25-30
30-35
35-40
f
5
10
15
20
15
10
5
------------N=80
15 marks
cf
5
15
30
50
65
75
80
1) Quartile deviation:
Coefficient of quaratile deviation= Q3-Q1/ Q3+Q1
Q3 is the size of 3N/4 or 80x3/4
Q3 lies in the class 25-30
Therefore Q3= l1+3N/4-cf
f
X i
= 25+ 60-50/15 x 5
= 28.33
Q1 is the size of N/4 or 80/4
Q1 lies in the class 15-20
Therefore Q1=l1 + n/4-cf/f x i
= 15+20-15/15 x 5
= 16.67
Therefore coefficient of Quartile deviation= 28.33-16.67/28.33+16.67
= 11.66/45
= 0.259
2) Bowley’s Quartile coefficient of skewness= Q3+Q1-2(median)/Q3-Q1
Median is the size of N/2 or 80/2 or 40 th item
Thus median lies in the class 20-25
By interpolation M= l1= N/2-cf/f x i
= 20+40-30/20 x 5 = 20+10/20 x 5
= 22.5
Q-3) Do Any Two A OR B OR C
20 marks
A). If a new drug has been found to be effective 40% of the time, then what is the
probability that in a random sample of 4 patients, it will be effective on 2 of them?
Find “Effective” as success and “Non-effective”.
P= 4( since the drug is effective 40% of the time)
q = (l-p) = 1-4 =6
x=2 n =4
10 marks
therefore p(x) = (n/x) (p)2 (q) 2
= 4!/2!2! (.4)2 (.6)2
= 6x .16 x .36
= 0.3456
B).Explain any with Example in brief
a) Addition Rule
OR
b) Multiplication Rule
OR
10 marks
c) Conditional Probability
C.) The probability that a student passes a test in Statistics is 2/3, and the probability that
he passes both a test in statistics and a test in mathematics is 1445. The probability that he
10 marks
passes the test in Mathematics?
Q-4)
A babysitter has 5 children under her supervision with average age of 6 years. But
individually, the age of each child be as follows:
X1 = 2
X2 = 4
X3 = 6
X4 = 8
X5 = 10
Calculate Population Mean and Standard Deviation.
N=5 as the no of children is 5
The population mean= E X/ N
= 2+4+6+8+10/5
=30/5 = 6
And standard deviation is as under:
Standard deviation= σ = Σ (x –µ)2/N)1/2
Now X = 2,4,6,8,10
And μ = 6,6,6,6,6
(X-μ) 2 = (2-6)2 = 16, (4-6)2 = 4, ( 6-6)2 =0, ( 8-6)2 = 4 , ( 10-6)2 = 16
Total = Σ X-μ) 2 = 40
Therefore σ =( 40/5)1/2
= (8)1/2
= 2.83
5 marks
OR
Explain
a) Null Hypothesis
OR
b) Alternative Hypothesis
5 marks