MCA- I Mid. Term Examination, April 2013
Subject: Statistical Methods
Maximum Marks:-50
Time Allowed: - Two Hours
Note: - Attempt question of all three sections as directed. Distribution of Marks is given with section
Setction - ‘A’
Objective Type Question
Note: - Answer all the questions. Each question carries 1 marks.
Q.1.
Cumulative frequency Curve is also known on:
a) Frequency
Q.2.
Q.4.
c) Give
b) Median
c) Mode
b) Mean – Mode = 2(Mean – Median)
c) Mean – Mode = 3 (Mean – Median)
d) Mean – Mode = 3(Median – Mean)
The median of the data 83, 54, 78, 64, 90, 59, 67, 72, 70, 73 is
b) 71
c) 72
d) 73
Match the following
(i) l + 4
b) Mode
(ii) ∑𝑛𝑖=1 𝑓𝑖 𝑥1 / ∑𝑛𝑖=1 𝑓𝑖
c) H.M.
(iii) 𝑙 + 2𝑓−𝑓 −1−𝑓 × 𝑖
f
×i
𝑓−𝑓
−1
1
1
1
2
1
1
d) Lower Quartile
(iv) 𝑥/ 𝑥 + 𝑥 +. . . + 𝑥
a) (ii), (iii), (iv) & (i)
b) (i), (ii), (iv) & (iii)
c) (i), (iii), (iv) & (ii)
d) (i), (iii), (ii) & (iv)
𝑛
Which of the following average is mathematical average.
b) Median
c) Mode
d) Partition Values
c) Leptokurtic
d) None of these
If P2 >3, then the curve is
a) Normal
Q.8.
N−F
a) A.M.
a) A.M.
Q.7.
d) None of these
a) Mean – Mode = Mean - Median
1
Q.6.
d) U-Shaped Curve
In moderately asymmetrical distribution, the empirical relation between mean, median & mode is
a) 70
Q.5.
b) Histogram
The most stable measure of Central tendency is
a) Mean
Q.3.
(10*1=10)
b) Platykurtic
Quartile Coefficient of Skewness is also known as
a) Karl Pearson’s Coefficient of Skewness
b) Bouley’s Coefficient of Skewness
c) Kurtosis
d) None of these
Q.9.
A Variable x takes values 1, 2, 3 ………… n each with frequency unity. The mean of the
distribution is:
a)
𝑛(𝑛+1)
𝑛
b) 2
2
c)
𝑛+1
d) None of these
2
Q.10. The Karl Pearson’s Coefficient of Skewness value lies between:
a) -1 and 1
b) -3 and 3
c) -2 and 2
d) None of these
Setction - ‘B’
(Short Answer Type Question)
Note: - Answer any two questions. Each question carries 05 marks.
Q.1.
Q.2.
(2*5=10)
Find the missing frequencies from the following table:
Expension (in Rs.)
:
0-20
20-40 40-60 60-80 80-100
No. of families
:
14
?
27
?
15
The details of runs gained by two batsmen Sachin and yuvi in different innings are as follows:
Sachin :
24
79
31
114
14
02
68
01
110
07
Yuvi
05
18
42
53
09
47
52
17
81
56
:
Which of the player is better run scorer?
Q.3.
Write short notes on the following
(a) Histogram
(b) Kurtosis
Setction - ‘C’
(Long Answer Type Question)
Note: - Answer any three questions. Each question carries 10 marks.
Q.1.
(3*10=30)
From the following frequency distribution, Computer 4th deale, 3rd Quartile, 94th percentile.
Class
:
0-4
4-8
8-12
12-14 14-18 18-20 20-25 ≥ 25
Frequency
:
10
12
18
7
5
8
4
6
Q.2.
In a frequency distribution, the mean is 1.5; Variance is 0.64, 𝛾1 is 0.3 and 𝛽2 is 2.5. Find 𝜇3 and
𝜇4 and also the first four moments about the origin.
Q.3.
Calculate the Karl Pearson’s Coefficient of skewness for the following frequency distribution
Class
:
0-5
5-10
10-15 15-20 20-25 25-30 30-35 35-40
Frequency
:
5
20
10
0
5
20
8
7
Q.4.
Define the skewness and kurtosis of a distribution. The first four moments about the working
mean 28.5 of a distribution are 0.294, 7.144, 42.409 and 454.98. Calculate the moment about the
mean. Also evaluate 𝛽1 , 𝛽2 and comment upon the skewness and kurtosis of the distribution.
Q.5.
Compute the mean, mode, S.D, and Coefficient of skewness for the following data:
Age Below
:
10
20
30
40
50
60
No. of person :
15
32
51
78
97
109