UNIT CODE		: 	MATH 130
UNIT TITLE	:	BASIC STATISTICS
INSTRUCTIONS
Answer question one and any other two questions
Question One (COMPULSORY – 30 Marks)
a.	Explain the difference between the following terms;
i)	Mutually exclusive and independent events
ii)	Qualitative and quantitative variables
iii)	Population and sample						(6 Marks)
b.	Given the data 66, 30, 34, 60, 20, 75, 42, 70, 34, 69.  Calculate
i)	Range									(2 marks)
ii)	Mean									(2 marks)
iii)	Median									(2 Marks)
iv)	Mode									(1 mark)
c.	A box contains 6 identical red, 4 identical blue and 5 identical yellow beads.  If a bead is drawn at random from the box.  What is the probability that it is;											(6 Marks)
(i)	Blue
(ii)	Yellow
(iii)	Red or blue
d.	A survey was carried out to find the different car color passing through KeMU gate on a Monday.  The results were as shown

Color of car	Red 	Blue 	White 	Black	
No. of cars	20 	30 	60 	10	

Draw a pie chart to represent this data					(5 Marks)
e.	The table shows the arithmetic mean and the standard deviation of marks of 3 students
	Arithmetic mean	Standard deviation	
Bosco 	12	2	
Jane	49	12	
Mary	50	15	

Calculate the coefficients of variation (CV) and compare the dispersion													(6 Marks)
Question Two (20 marks)
The table below shows the expenditure by KeMU students during a field trip
Amount Ksh.	0-99	100-199	200-299	300-399	400-499	500-599	
Frequency 	30	38	50	31	22	13	

a.	Calculate
(i)	The mean								(4 Marks)
(ii)	Median								(4 Marks)
(iii)	Variance								(4 Marks)
(iv)	Standard deviation						(2 Marks)
b.	Draw a Histogram of the data above					(6 Marks)

Question Three (20 marks)
a.	(i) Define kurtosis								(2 Marks)
(ii) Name three types of Kurtosis and using a diagram differentiate between them										(5 Marks)
b.	Given the following set of data
X	10	20	30	40	50	60	70	
Y	34	46	48	53	55	63	65	

(i)	Determine the Pearson’s product moment coefficient of correlation(r )											(11 Marks) 
(ii)	Comment on the relationship between X and Y		(2 marks)
Question Four (20 marks)
a.	In a family, the probability that a child is female is 0.6.  if there are three children in the family, what is the probability that
(i)	Exactly 2 are girls							(3 Marks)
(ii)	At least 1 is a boy							(4 marks)
b.	The table below show distribution of marks of student in a physics exam

Marks	30-39	40-49	50-59	60-69	70-79	80-89	90-99	
Frequency	1	4	14	20	22	12	2	

Calculate 
i)	Variance									(8 marks)
ii)	Standard deviation							(2 marks)
c.	State three importance of statistical knowledge in research	(3 Marks)