Mastering Quantitative Methods: Essential Concepts, Calculations, and Data Analysis Techniques

Quantitative Methods 1
Quantitative Methods
Student’s Name
Student’s Number
University
Module Code
Module Name
Date

Quantitative Methods 2
Question 1
a) Population :200 voters
b) Sample:
48% of 200 = 96 voters
c) Parameter :over 50% of registered voters voted in favour of the politician
d) Statistic: voters for the politician i.e. 48% sample of the registered voters
e) The statistic is 48%
f) The parameter is 50%
Question 2
a)
Mean = total sum/ number of items
= 14+8+3+2+6+4+9+13+10+12/10
= 81/10
=8.1
Median
Arrange from smallest to largest
2,3,4,6,8,9,10,12,13,14
= (8+9)/2
8.5
Mode
Not applicable since there is no number that is repeated
b)
x x-xbar
(x-
xbar)2
4 -1 1
5 0 0
3 -2 4
6 1 1
5 0 0
6 1 1
5 0 0
6 1 1
40 8
5

Quantitative Methods 3
= 8/8
=1
Variance = S2
= 1
Question 3
About 68% of the data are in the interval of 120 +- 1(30) = [80, 150]
About 95% of the data are in the interval of 120+- 2(30) = [60, 180]
About 99.7% of the data are in the interval of 120 +- 3(30) = [30,210]
a) None are less than 30
b) 95%
c) Over 68%
Question 4
Qi = [i(n+1)/4]th
39 ,43, 51,52,60,61,64,71,73,88
Q1 = 1 (10+1)/4
= 2.75th
2nd observation = 43
3rd observation = 51
Q1 = 43 + 0.75 (51-43)
= 49
Q2 = 2(10+1)/4
= 5.5th
5th observation = 60
6th observation = 61
Q1 = 60 + 0.5 (61-60)
= 60.5
Q3 = 3 (10+1) /4