INSTRUCTIONS TO CANDIDATES
1. The exam is Closed Book.
2. Attempt any 5 questions out of 6
3. Calculator is allowed.
1. The following data present number of units of spare parts sold during last 50 days in a company: [5+5+5+5]
100 173 202 178 147 102 153 197 127 101
157 185 190 116 172 148 213 130 165 111
141 149 206 175 123 128 144 168 109 167
100 163 150 154 130 143 186 166 139 149
108 119 183 151 114 135 191 137 129 258
(a) Prepare a frequency distribution starting from 100 with class width 20. Draw a histogram for the frequency distribution.
(b) Draw a frequency polygon for the same frequency distribution.
(c) Calculate the cumulative frequencies for the frequency distribution in Q(a) and draw an ogive for the data.
(d) Calculate mean number of units sold for the above data.
2. The following data present scores of 100 students in one of their examination. [3+8+9]
Scores in an Exam Less than 15 15-20 20-25 25-30 30-35 35-40 40-45 More than 45
number of students 3 13 16 17 28 13 7 3
(a) Can you calculate mean marks for the above data? If yes, calculate the mean value. Else state your reasons for not calculating mean.
(b) Can you calculate median and mode marks for the above data? If yes, calculate the median and mode values. Else state your reasons for not calculating them.
(c) Calculate 3rd quartile (Q3), 6th decile (D6) and 38th percentile (P38) for the given data.
3. (a) What do you mean by measures of dispersion? Mention names and formulae of any five measures of dispersion. [6+8+6]
(b) The following data represent the time (in minutes) to process customer complaints in a national bank in its two branches, Main City Branch and Countryside Branch:
Main City Branch 1.48 1.75 0.78 2.85 0.52 1.6 4.2 3.97 1.48 3.1
Countryside Branch 7.55 3.75 0.1 1.1 0.6 0.52 3.3 2.1 0.58 4
Calculate standard deviation for both the branches and comment on which branch has less variation in processing the complaints.
(c) Data have been collected on three variables, viz., price of commodity (in Rs.), number of purchases (in units) and shelf space (in square feet) as presented below. Use an appropriate measure of dispersion and comment on which dataset has got highest level of variation.
sample size
mean standard deviation
I. price of commodity (in Rs)
10
436
23.4
II. number of purchases (in units)
10
26
5
III. shelf space used for commodities (in square feet)
10
4
1.5
4. Answer the following: [16+2+2]
(a) Compare and contrast the three measures of central tendency, mean, median and mode with respect to the criteria of ideal measure of central tendency. Discuss at least 8 criteria.
(b) For a moderately symmetric distribution, if mean=43, median=40, find mode value.
(c) For a symmetric distribution, if mode=26, calculate mean and median.
5. What do you mean by correlation between two variables? For the following data calculate Karl Pearson’s correlation coefficient. Comment on the nature of relationship between two variables. [20]
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