Reference no: EM132846898

QUESTION ONE

a) You have collected that data below on the waiting times (in seconds) in your attempt to analyze the waiting times at a major bank in Nairobi

10 10 12 15 20 24 12 30 35 25 25 18

15 11 18 45 65 23 55 40 12 14 50 50

51 12 13 13 14 21 22 21 21 24 40 31

32 30 16 16 17 17 22 61 54 53 52 52

65 65 63 62 50 41 42 33 32 21 21 22

i. Construct a stem and lead diagram for the above data;

ii. From the stem and leaf diagram in a(i) above and using the Sturges Rule construct a grouped frequency distribution;

b) Using the grouped frequency distribution in a(ii) above find the following

i. Arithmetic mean and the corresponding standard deviation

ii. Coefficient of variation

iii. Geometric mean

QUESTION TWO

Kenya Commercial Bank has received complaints from a number of its customers regarding the waiting time problem at its branches. The bank has therefore given you a consultancy to try and assess the nature of the problem and recommend solutions. Towards this end, you have collected data on waiting times by 50 customers who visit the Bank's Kipande house branch during two selected time windows: 9-12 and 2-4pm. The waiting times are as shown below:

9-12PM WAITING TIMES (Xm)

92 39 78 67 68 58 80 89 92 69 66 56 88 81 70 73 63 55 67 68 80 90 56 75 74 56 47 59 64 89 39 51 87 89 76 59 72 80 95 64 53 43 61 71 38 44 88 62 64 62

2-4 PM WAITING TIMES (Xa)

16 8 10 17 25 34 42 18 24 18 45 33 40 3 20 12 10 15 16 26 16 14 18 25 37 49 52 6 32 54 20 20 66 21 5 8 62 46 24 15 20 18 8 10 25 10 27 16 37 45

a) Construct a Stem and Leaf diagrams for each of the two time windows and interpret the result:

b) Using the Stem and Leaf diagrams for each of the time windows constructed in (a) above, construct corresponding grouped frequency distribution tables given k=1+3.322Log(N) and C=/R/k

c) From each the resulting tables in (b) above for each of the time windows, find the coefficient of variation, CoVm and COVa for the 9-10 and 2-4 time windows respectively and correctly interpret your results ( ) where S is standard deviation and is the mean waiting time).

QUESTION THREE

a) You have collected that data below on the wages (in thousands on Ksh.) in a sector in your attempt to analyze the distribution of sectorial wages

10 10 12 15 20 24 12 30 35 25 25 18

15 11 18 45 65 23 55 40 12 14 50 50

32 12 13 13 14 21 22 21 21 24 40 31

32 30 16 16 17 17 22 61 54 53 52 52

65 63 62 50 41 42 33 32 21 21 22

Using the Sturges Rule construct a grouped frequency distribution;

b) Using the grouped frequency distribution in a(ii) above find the following

i. Harmonic mean

ii. 1st and 2nd quartile and hence the interquartile range

iii. 10th and the 30th percentile

c) On the basis of the grouped frequency distribution in a (a) above construct the following

i. Histogram hence derive an appropriate measure of central tendency verifying your answer using an appropriate analytical approach (Formula)

ii. The less than ogive and hence derive an appropriate measure of central tendency verifying your answer using an appropriate analytical approach (Formula)