**MAASAI MARA UNIVERSITY**

**SCHOOL: Business and economics**

**COURSE NAME: BUSINESS STATISTICS**

**COURSE CODE: CHR 101**

**QUESTION ONE**

a) Define the following

i. The arithmetic mean (2 Marks)

ii. Class limits (2 Marks)

iii. The semi interquartile range (2 Marks)

iv. KURTOSIS (2 Marks)

v. Skewness (2 Marks)

b) Write short notes on FOUR applications of statistics in business (4 Marks)

c) In 1995 five firms registered the following economic growth rates; 26%. 32% 41% 18% and 36%.Calculate the GM for the above values (4 Marks)

d) State the advantages and disadvantage of using the following measures of dispersion

i. The arithmetic mean (2 Marks)

ii. The median (2 Marks)

e) State THREE Measures of Dispersion (3 Marks)

**QUESTION TWO**

a) The economic growth rates of five countries were given as 20%, 15%, 25%, 18% and 5%

Calculate the harmonic mean (3 Marks)

b) In a given exam the scores for 10 students were as follows

Required

Determine the absolute mean deviation (4 Marks)

c) In a given farm located in the UK the average salary of the employees is £ 3500 with a standard deviation of £150. The same firm has a local branch in Kenya in which the average salaries are Kshs 8500 with a standard deviation of Kshs.800. Determine the coefficient of variation in the 2 firms and briefly comment on the degree of dispersion of the salaries in the 2 firms. (4 Marks)

d) State FOUR advantages of using Mode as a measure of central tendency (4 Marks)

**QUESTION THREE**

a)The following table shows the part-time rate per hour of a given no. of laborers in the month of June 1997.

Rate per hr (x) Shs No. of labourers (f)

Calculate the

i. Mean (3 Marks)

ii. Median (3 Marks)

iii. Variance (4 Marks)

iv. Standard deviation (2 Marks)

b) State three advantages of using Standard Deviation as a measure of dispersion (3 Marks)

**QUESTION FOUR**

The following table shows the levels of retirement benefits given to a group of workers in a given establishment.

Required

i. Determine the semi interquartile range for the above data (3 Marks)

ii. Determine the minimum value for the top ten per cent.(10%) (3 Marks)

iii. Determine the maximum value for the lower 40% of the retirees (3 Marks)

iv. calculate the 90th percentile (3 Marks)

b) State Three types kurtosis (3 Marks)

**QUESTION FIVE**

a) Find the moment coefficient of the following distribution

(4 Marks)

b) The data given below indicates the prices and production of some horticulatural products in Central Territory:

Required:

Calculate the increase or decrease in prices from 1980 on the basis of the following indices:

a) Mean relatives (3Marks)

b) Laspeyres index (3 Marks)

c) Paasche index (3 Marks)

d) Fishers index. (2 Marks)