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Question 1:                                                                                                                   Marks: 5+2=7
a)   Following are the heights (in centimeters) of 45 female high school students. Prepare a frequency distribution of the data where the class width is 5, the number of classes is 6 and the smallest observation is 148. Also obtain the relative frequency and relative cumulative frequency.
170, 151, 154, 160, 158, 154, 171, 156, 160, 157, 160, 157, 148, 165, 158, 159, 155, 151, 152, 161, 156, 164, 156, 163, 174, 153, 170, 149, 166, 154, 166, 160, 160, 161, 154, 163, 164, 160, 148, 162, 167, 165, 158, 158, 176.

b)     Which level of measurement (scale of measurement) is suitable for the following data in each example?
i) The lake Saif-ul-Muluk is 10,578 feet above from the sea level.
ii) If customers go to the shop for buying shoes and try different size of shoes. The sizes of shoes are 7B, 10D and 12E.
iii) The numbering on T-shirts of players in the cricket team.
iv) The weight of the person is 68 kg.
Question 2:                                                                                                                   Marks: 5+3=8

a)      Find the median, harmonic mean and 23^rd percentile for the following frequency distribution.

Class Boundaries	Frequency
145 – 150	4
150 – 155	6
155 – 160	28
160 – 165	58
165 – 170	64
170 – 175	30

b)     Explain the concept of Geometric mean? Also find the geometric mean for the following data.
18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 23, 24, 27, 30, 36
Solution: Working on Solution