# STA301 VU Current Assignment Solution No. 1 Fall 2012

STA301 Assignment No.1 Last Date: 7th November, 2012

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 23rd 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

2 b)

Q NO.2 (B)

Concept of Geometric Mean

The geometric mean is well defined only for sets of real positive numbers. In Geometric mean is calculated by multiplying all the numbers and taking th nth root of the total.

The formula of Geometric mean is

log G =                    Σ log X

________________

N

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

X                                                         Log X

18                                                        1.2553

19                                                        1.2788

19                                                        1.2788

19                                                        1.2788

19                                                        1.2788