Mathematics Homework Assignment: Solutions and Detailed Explanations

This document presents a comprehensive solution to a mathematics homework assignment. The assignment covers a variety of mathematical concepts including calculating the range of a data set, finding the sum of the smallest and largest numbers, solving percentage problems related to a business venture, determining the minimum score needed to achieve a first-class degree, converting fractions to decimals, calculating percentage increases, and identifying the mode of a data set. Each question is presented with a detailed solution, explaining the steps and methods used to arrive at the answer. The solutions are well-structured and easy to follow, making this a valuable resource for students seeking to understand and master these mathematical concepts. The assignment includes references to support the solutions provided. This resource aims to help students understand and solve similar problems effectively.

Running head: Maths
Maths
Name of student:
Name of university:
Authors Note:

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Table of Contents
Q1...............................................................................................................................................3
Solution 1...............................................................................................................................3
Q 2..............................................................................................................................................3
Solution 2:..............................................................................................................................3
Q3...............................................................................................................................................3
Solution 3...............................................................................................................................4
Q4...............................................................................................................................................4
Solution 4...............................................................................................................................4
Q5...............................................................................................................................................5
Solution 5:..............................................................................................................................5
Q6...............................................................................................................................................5
Solution 6:..............................................................................................................................5
Q7...............................................................................................................................................6
Solution 7...............................................................................................................................6
Q8...............................................................................................................................................6
Solution 8...............................................................................................................................6
References..................................................................................................................................7

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Q1.
What is the range of the following data set?
31 24 9 0 12 -1 14 -7
Select one:
a. -24
b. 24
c. -27
d. 38
Solution 1:
Range = Difference of largest and smallest value from the data = (31- (-7)) = 38. (Gupta and
Gupta 2017)
Q 2.
What is the sum of the smallest and the largest number from the following data set:
0.09 ; 0.85 ; 0.678 ; 0.80
Select one:
a. 0.94
b. 0.768
c. 1.65
d. 0.89
Solution 2:
Smallest number + Largest number = 0.09+0.85 = 0.94
Q3.
Peter recently invested £120,000 in a new business venture and spent 50% of his investment
on equipment, 30% on rent and 10% on stock to sell.
How much money does he have left over?
Select one:
a. £60,000

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b. £12,000
c. £108,000
d. £1,200
Solution 3:
Amount of money invested on equipment = 50
100 ×120,000
= 60,000
Amount of money invested on rent = 30
100 ×120,000
= 36,000
Amount of money invested on stock = 10
100 ×120,000
= 12,000
The amount of money left for him = (120,000 – 60,000- 36,000- 12,000)
= 12,000
Q4
to be awarded a first class Honours on a Degree programme, you must have a mean (an
average) of 70% overall in the final six subjects.
So far your scores in 4 subjects are 63, 67, 70, 71 and 69.
What is the minimum score must you achieve in the final subject, in order to attain a first
class degree?
Select one:
a. 70
b. 75
c. 80
d. 85

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Solution 4
Let the minimum mark needed be x.
We need, (63+67+70+71+69+x ¿ /6
≥ 70
∴ 340+ x ≥ 420
⟹ x ≥ 80
So, minimum of 80 marks need to be scored to keep a mean of 70.
Q5.
41/333 expressed as a decimal is:
Select one:
a. 0.123231
b. 0.012312
c. 0.00123
d. 0.123
Solution 5:
41/333 = 0.123123
Q6.
A price of a house increased from £350,500 to £375,500. What was the percentage increase
in the price of this house?
Select one:
a. +17.5%
b. +11.5%
c. +7.14%
d. -1.74%
Solution 6:
Percentage increase in the price of the house = 375,500−350,500
350,500 × 100
= 7.13

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Q7.
Which measure of central tendency would you use to find out the favourite academic subject
of your classmates?
Select one:
a. Median
b. Range
c. Mode
d. Mean
Solution 7:
The favourite subject would be the one that appears in the dataset with the highest frequency.
The number with highest frequency in the dataset is the mode of the data. Therefore, we will
calculate the mode.
Q8.
What is the mode of the following data set?
12.075, 12.076, 13.075, 19.120, 012.076, 13.057, 12.015, 011.213,
Select one:
a. 12.076
b. 011.213
c. 13.075
d. 12.075
Solution 8:
Mode of a dataset is the data with the most frequency ( Groebner et al. 2013). From the
data it is seen that that number is 12.076 with frequency 2.
Previous page

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References:
Groebner, D.F., Shannon, P.W., Fry, P.C. and Smith, K.D., 2013. Business statistics. Pearson
Education UK.
Gupta, K.R. and Gupta, M.P., 2017. Business statistics. Atlantic Publishers & Distributors.