Question

Question 6
(a) Explain the difference between class limit and class boundaries. [2 marks]
(b) Use the frequency table, Table 1, overleaf to answer the following questions:
Table 1

X	f
0-9	3
10-19	14
20-29	11
30-39	5

(i) What is the class width?
(ii) What is the sample size?
(iii) What is the lower class limit of the first class?
(iv) What is the lower class boundary of the first class?
(i) What is the class width?
(ii) What is the sample size?
(iii) What is the lower class limit of the first class?
(iv) What is the lower class boundary of the first class?

Question 7
Use Table 1 above to calculate:
(a) the mean [3 marks]
(b) the median [4 marks]
(c) the mode [4 marks]
(d) the first quartile [4 marks]
(e) the standard deviation. [3 marks]

Answer 1

Ans:

(i) class width=10-0=10
(ii) sample size=3+14+11+5=33
(iii) lower class limit=0
(iv) lower class boundary of the first class=0-0.5=-0.5

X	mid point(m)	f	m*f	(m-19.955)^2*f
0-9	4.5	3	13.5	716.571
10-19	14.5	14	203	416.598
20-29	24.5	11	269.5	227.227
30-39	34.5	5	172.5	1057.785
Total		33	658.5	2418.182

(a)mean=2418.182/33=19.955

(b) median will fall in the class 10-19
(c) mode will also be in the class 10-19,as highest frequency.
(d)first quartile will also be somewhere in 10-19
(e) standard deviation==SQRT(2418.182/(33-1))=8.69