# STA301 Statistics and Probability Assignment 1 Solution Spring 2013

Assignment No: 1 (Lessons 1-9)

Question 1:                                                                                                              Marks: 4+3=7

1. Given the following frequency distribution:
 Class Limits Frequency 118 – 126 3 127 – 135 5 136 – 144 9 145 – 153 12 154 – 162 5

Construct the columns of Class Boundaries, Relative Frequency, Mid points and

Cumulative frequency.

1. The ages of 22 patients admitted to a certain hospital during a particular week were as

follows:

66, 73, 68, 54, 25, 38, 67, 69, 74, 53, 52, 72, 55, 75, 37, 24, 13, 12, 11, 26, 39, 23

Construct a Stem and Leaf display for the above data.

Solution:

 Class limit Class boundaries Mid points Frequency Cumulativefrequency Relative frequency 118 – 126 117.5 – 126.5 122 3 3 3/34=0.088 127 – 135 126.5 – 135.5 131 5 8 5/34=0.147 136 – 144 136.5 – 144.5 140 9 17 9/34=0.264 145 – 153 144.5 – 153.5 149 12 29 12/34=0.352 154 – 162 153.5 – 162.5 158 5 34 5/34=0.147

Question 2:                                                                                                              Marks: 6+2=8

1. Ten students (graduates and undergraduates) are enrolled in the course on statistics. Their weights are given below:

52, 63, 73, 58, 88, 72, 60, 76, 69, 74

Calculate Arithmetic mean, Geometric mean and Harmonic mean for the above data.

Solution:

Arithmetic Mean = 68.5

Geometric Mean = 67.78 and

Harmonic Mean = 67.02

b.    Which scale of measurement is more suitable in the following examples?

• Religion can be categorized as Jewish, Muslim, Christian, Buddhist and “Other”.
• A teacher ranks the students according to their oral language skills.
• The number of minutes of overtime work that employees perform.
• The number of questions asked by a customer during a simulated encounter with a salesperson.

Examples: Suitable measurements
Religion can be categorized as Jewish, Muslim, Christian, Buddhist and “Other”.Nominal
A teacher ranks the students according to their oral language skills. Ordinary/ranking
The number of minutes of overtime work that employees perform. Interval
The number of questions asked by a customer during a simulated encounter with a salesperson.interval