SST 101: INTRODUCTION TO PROBABILITY AND STATISTICS
1. A business lady buys her products from three companies. The following is a summary
of her savings in thousands of Kenya Shillings from buying the products from the three
companies for the past one week.
Measure Company
A B C
Mean 19.50 32.60 22.40
Variance 5.60 5.67 7.20
Determine which company that she should continue buying from. Why? (5 marks)
2. The first three moments of a distribution about a value 4 of the variable are 1, 20 and
40. Find the mean, variance and the third moment about the mean. (6 marks)
3. The median and standard deviation of 50 observations are 25 and 6 respectively. Find
the coefficient of skewness if the sum of the observations is 900. Comment on your
answer. (2 marks)
4. The data below gives the volume of liquor (in liters) in five different cans.
12.3 12.1 12.2 12.3 12.4. Compute the geometric mean. (1 mark)
5. Consider the following data for a group of ten students showing the number of times
each was late for Mathematics lectures in a semester.
6 7 5 8 14 6 5 4 6 9
(a) Calculate the second, third and fourth central moments. (4 marks)
(b) Using the results in (a) above obtain the Skewness and Kurtosis of this data and
comment on your results. (4 marks)
6. The following frequency distribution shows the weights in kilograms of a population
of 100 monkeys in a certain forest.
Weight (kg) Number of monkeys
10 – 20 14
20 – 30 23
30 – 40 27
40 – 50 21
50 – 60 15
Estimate the quartile coefficient of Skewness and interpret the value obtained. Show your
calculations correct to two decimal places. (8 marks)
1. A business lady buys her products from three companies. The following is a summary
of her savings in thousands of Kenya Shillings from buying the products from the three
companies for the past one week.
Measure Company
A B C
Mean 19.50 32.60 22.40
Variance 5.60 5.67 7.20
Determine which company that she should continue buying from. Why? (5 marks)
2. The first three moments of a distribution about a value 4 of the variable are 1, 20 and
40. Find the mean, variance and the third moment about the mean. (6 marks)
3. The median and standard deviation of 50 observations are 25 and 6 respectively. Find
the coefficient of skewness if the sum of the observations is 900. Comment on your
answer. (2 marks)
4. The data below gives the volume of liquor (in liters) in five different cans.
12.3 12.1 12.2 12.3 12.4. Compute the geometric mean. (1 mark)
5. Consider the following data for a group of ten students showing the number of times
each was late for Mathematics lectures in a semester.
6 7 5 8 14 6 5 4 6 9
(a) Calculate the second, third and fourth central moments. (4 marks)
(b) Using the results in (a) above obtain the Skewness and Kurtosis of this data and
comment on your results. (4 marks)
6. The following frequency distribution shows the weights in kilograms of a population
of 100 monkeys in a certain forest.
Weight (kg) Number of monkeys
10 – 20 14
20 – 30 23
30 – 40 27
40 – 50 21
50 – 60 15
Estimate the quartile coefficient of Skewness and interpret the value obtained. Show your
calculations correct to two decimal places. (8 marks)
