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Seat No.: Enrolment No.:
GUJARAT TECHNOLOGICAL UNIVERSITY
BPLAN SEMESTER • EXAMINATION WINTER 2016
Subject Code: 1015504 Date: 03/01/2017
Subject Name: Statistics and Quantitative Methods in Planning I
Time:10:30 AM to 12:30 PM Total Marks: 50
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Multiple choice question
1. Earthquake is example of which type of variation?
a. Secular Trend
b. Cyclic variation
c. Seasonal variation
d. Irregular variation
2. which are Mean and Mode in this data set?
a. 4 and 9
b. 6 and 7
c. 6.18 and 7
d. None
3. Average speed can be calculated using which one of this method?
a. Arithmetic Mean
b. Harmonic Mean
c. Geometric Mean
d. Weighted Mean
4. In Standard normal distribution, if value of standard score of any particular observation is zero. So what dose it suggest?
a. Value of that observation is equal to mean.
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b. Value of that observation is greater than to mean.
c. Value of that observation is less than to mean.
d. None of the above.
5. Which one of these is not type of non-probability sampling?
a. Deliberate (Quota) sampling
b. Convenience sampling.
c. Systematic sampling.
d. Purposive sampling.
6. Which of the following is Not Measure of central tendency?
a. Harmonic mean.
b. Median.
c. Mode.
d. All these are measure of central tendency

true false
1. In simple random sampling, each observation has an equal probability of getting selected.
2. While calculating the mean of group data, we assume that every value in each class is equal to mid point of that class.
3. Shape of bell curve in standard normal probability is not always symmetrical.
4. Value of standard deviation is distance of all the observations from the mean line.
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Q.2

Table below, shows monthly expenditure of person A and Person B on different things. Represent this data with single Bar Graph. Now, if monthly income for both the person A and B are 20,00 and 25,000 respectively. Drew Inferences for which of these person is spending more on "Books" with help of Pie Chart. (Remaining salary is monthly savings)
No.
Expenses
Person A
Person B
1
Food
4000
4500
2
House Rent
3500
4000
3
Travel
2000
2250
4
Books
3000
3250
5
Cloths
2500
4000
05

Municipality of the city "Planningpur" and "Archidabad" are spending certain
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amount on various services. The services are mentioned below.
No.
Services
Planningpur
Archidabad
1
Roads
15 Cr.
17.5 Cr.
2
Water Supply
10 Cr.
8 Cr.
3
Solid Waste Management
5 Cr.
4.5 Cr.
4
Public Buildings
4 Cr.
6 Cr.
5
Maintenance
6 Cr.
4 Cr.
Now, State Govt. of GTU wants to know which city is spending money efficiently. For that, they have given certain weightage to different services are as described. Road Water Supply Solid Waste Management Public Buildings Maintenance 20%
OR

In one standard normal distribution, population mean is 800, and standard deviation is 100, find out the probability for given situations. (Include diagram in answers) (Use the table provided for Z-test)
Total probability of observations above 650.
Total probability of observations between 700 and 900.
Total probability of observations below 950.
05
Q.3

Write short note
1. What is Data and what is different types of data?
2. Explain: Secular Trend, Seasonal Variation( With Example)
10
OR
Q.3

Write short note
1. Explain: Simple random sampling, Stratified sampling, Systematic sampling.
2. What is time series analysis? And what are the components of Time series analysis?
Q.4

Arrange the given data set in ascending or descending order and construct a frequency distribution table. Draw a histogram and cumulating frequency graph. (min. 5 groups)
60
72
126
110
91
115
112
80
66
101
75
93
129
105
113
05
4
121
99
87
119
111
97
89
114
128
84
114
108
78
68
125
Q.4

Short Note: Explain any one method for calculating measure of secular trend with proper example. (Freehand curve, Semi average Method, Moving average Method)
05
OR
Q.4

Short note: What is statistics and what is the importance of statistics in planning field?
05
Q.5

The given data is an annual income of a planning firm over a period of 5 years, calculate average increase in Income for this firm.
Year
Income
2009
1,00,000
2010
1,50,000
2011
1,75,000
2012
1,60,000
2013
2,10,000
05
OR
Q.5

1. Calculate the Population Variance and Population standard deviation for given dataset.
Class
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
100-109
110-119
120-129
Frequency
4
7
8
10
11
18
13
10
9
6
3
1
05

For XYZ technical institute, there are three different branches of Planning, Architecture and Engineering. Now Management of the institute has divided every student in three categories based on their performance. The categories are: Excellent, Average and Poor.
Now, as shown in given table,
If any one student is selected randomly, then what is the probability of that student is from planning or his performance is poor.
Branch
Planning
Architecture
Engineering
Performance
Excellent
5
8
12
Average
12
15
28
Poor
3
7
10
05

5
Standard Normal Probability distribution between Mean and Value of