BUSINESS STATISTICS

BMA2202 BUSINESS STATISTICS 1

INSTRUCTIONS:

• ATTEMPT ALL QUESTIONS
• ADHERE TO SUBMISSION DEADLINE

QUESTION ONE

The following table gives profits (in ten thousands of shillings) of two supermarkets over duration of one year.

Month	NAIVAS	TUSKEYS
January	683	294
February	504	347
March	158	210
April	294	242
May	431	725
June	620	473
July	431	557
August	105	158
September	252	368
October	588	599
November	966	1040
December	1260	1428

Required:

1. Compute the coefficient of variation for each supermarket.
2. Indicate for which supermarket the variability of profits is relatively greater

QUESTION TWO

1. The following data relates business turnover and staff of fast moving consumer goods company EAI Ltd:

Year	1993	1994	1995	1996	1997	1998	1999	2000
Business turnover in Millions of shillings	45	50	60	75	80	110	150	170
Staff	2,600	3,000	3,100	3,530	3,850	4,300	5,870	7,150

Required:

1. Fit an appropriate regression equation.                                                                                       
2. Estimate the staff requirement when business turnover reaches Sh.200 Million.                             

QUESTION THREE

The managers of an import agency are investigating the length of time that customers take to pay their invoices, the normal terms for which are 30 days net. They have checked the payment record of 100 customers chosen at random and have compiled the following table:

Payment in	Number of customers
5 to 9 days	4
10 to 14 days	10
15 to 19 days	17
20 to 24 days	20
25 to 29 days	22
30 to 34 days	16
35 to 39 days	8
40 to 44 days	3

Required:

1. Calculate the arithmetic mean.                     
2. Calculate the standard deviation                  
3. Construct a histogram and insert the modal value.
4. Estimate the probability that an unpaid invoice chosen at  random will be between 30 and 39 days old.                    

QUESTION FOUR

A survey by Marketing Society here in Kenya found out the following buying habits of household air conditioners considered a luxury.

Gross income per month	Number of consumers who buy Air conditioner
Up to 5,000	2
5,001 – 10,000	15
10,001 – 15,000	25
15,001 – 20,000	28
20,001 – 25,000	33
25,001 – 30,000	35
30,001 – 35,000	38
35,001 and above.	40

Required:

1. Calculate the arithmetic mean, median and mode.
2. Does the survey show that the luxury item is consumed by high-income earners? Show your answer by calculating appropriate measure of skewness.

QUESTION FIVE

1. Using a well labeled diagram, explain any two features of a negatively skewed distribution                                                                                                             
2. The shelf life of a product has a mean, µ = 10 days and a standard deviation, σ =3 days. Assuming a normal distribution, determine the probability of a product lasting for;
3. Between 7 days and 13 days                                                     
4. Fewer than 7 days                                                                    
5. The weight of 15 parcels recorded at the GPO was as follows:

16.2, 17,20,25,29,32.2,35.8,36.8,40,41,42,44,49,52,55. (inkgs)

Determine the semi interquartile range for the above data.           

QUESTION SIX

1. Consider the following stem and leaf plot.

            1          2          6          9         

2          0          2          6          8          8          8          9

3          1          3          7

4        0

5          6          7          9          9

6         

7          3          4          4          6          7         

8          1          3

Key:   1   2        represents 12

Required:

1. State the mode and the median of this data                           
2. Compute the mean and the variance                                                

QUESTION SEVEN

(a). For a period of three years accompany monitors the number of units of output per quarter and the total cost of producing the units. The table below shows their results.

Units	total cost
(x)	(y)
14	35
29	50
55	73
74	93
11	31
23	42
47	65
69	86
18	38
36	54
61	81
79	96

1. Draw a scatter diagram of these data                                                      
2. i.  Calculate the equation of the regression line of  y on x              

ii.  draw this line on your scatter diagram.                                                

3. The selling price of each unit of output is £ 1.6. Use your graph to estimate the level of output at which the total income and total cost are equal. Give a brief interpretation of the value.                                                                
4. Using a clearly labeled diagram, show the position of the mode, mean and median of a positively skewed distribution.             

QUESTION EIGHT

Outline the merits and demerits of the various measures of central tendency