1) A businessman has six business premises A, B, C, D, E and F. He keeps records of monthly net profits realised from these premises.

1) A businessman has six business premises A, B, C, D, E and F. He keeps records of monthly net profits realised from these premises. A pie-chart for last month's profits shows that 24 degrees represented the net profit realised from D. The total net profit from the six premises was £7200. He wishes to donate 10% of the total net profits realised from A, B, C and E to a particular children's home. Determine the amount he will donate.

2) The arithmetic mean of 100 observations collected by a researcher was 0.2gm. Afrequency distribution based on the actual observations was prepared. The frequencies of the lowest and the highest observations were f1 and f20 respectively. Check if the following statements are correct given that ∑Xi 2 fi  = 504

     (i)      1/100  ∑ {(Xi - Ẍ)2 fi  + 1 } = 6      (ii) 10 ∑ (Xi + 0.2)fi  = 4

     (iii)     ∑ {3Xi (Xi - Ẍ) fi  -  (Xi  - Ẍ) fi  - 50 } = 0

3) The following figures (in £'000) are amounts borrowed by various clients from a particular bank for a certain period.

       10   40   20   12   17   27   30   28   1    32 

        20   13   22   41   23   33   50   18   30  27

       36   9   16     3   22   40   34   24    8  19   

       25   16   27   14   31   19   20   36    6   42

       13   32   24   29   45   25  43   38    50  15

(i) Summarise the data in a frequency distribution based on classes of size 10. Use excusive method of data classification, taking the upper boundary of the highest class as 60.

(ii) Represent your answer to (i) by a less-than ogive and a frequency polygon.

4) Ten observations X1 ,  X2 , X3 , .......X10 were collected. Their sum was found to be 50 while the sum of their squares was found to be 800. If Ẍ is their arithmetic mean, determinethe values of the following expressions.        

            (i) ∑ (Ẍ - Xi)    (ii)  1/10 ∑{Xi  - 2Ẍ)2 + 1}

5) Weekly sales from 100 different shops were classified using a frequency distribution based on various classes. Data in the frequency distribution was coded using the relation

         di   =   1/200( Xi  - 10000),  where Xi is the ith class mark (in ksh).

The table of the codes and their respective frequencies was as follows:

code

 -2

 -1

 0

  1

  2

frequency

 10

 22

 38 

 15

 14

(i) Determine the mean of the sales from the 100 shops.

(ii) Prepare the frequency distribution of the sales.

6) The following data was extracted from an economics journal. 

Class(£'000)

0 - 5

5 - 10

10 - 15

15 - 20

20 - 25

25 - 30

30 - 35

frequency

 10

  4

  4

  10    

   6

   8

   7

​  

(i) Check if the difference between the median and the mode is only £250. 

(ii) It was later discovered that group £35000 - £40000 was left out when extracting the information. With this group included, the 10th percentile was found to be £2500. Determine the frequency of the omitted group.

7) A junior accountant of a particular supermarket was asked to give a summary of daily profits realised for a period of time. He presented his data as follows:

Profit (ksh'0000)

0 - 4

4 - 8

8 - 12

12 - 16

16 - 20

20 - 24

24 - 28

No. of days

 10

  20

 8

  30  

  7

  13

   12

(i) Check if the mean profit of the displayed data is ksh136400.

(ii) Further scrutiny of the raw data revealed that the frequency of the groups '8 - 12' and '16 - 20' were not as indicated. With the correct frequencies, the median and the mode were given as ksh140000 and ksh144000 respectively. Determine the correct frequencies.