Mathematics

# Problem based assignment- Mathematical skills for Business

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Assessment Type

Course Work

Word Count

1000 words

Subject

5 Days

## Assignment Criteria

.    The sales people at Archway's Car Depot earn commission based on how many and what types of cars they sell. The table below shows the profit y made by ten Archway's Car Depot salespeople after selling x cars.

Number of cars sold    Profit(£)
1    3,500
2    13,000
3    10,000
3    5,700
4    16,500
5    4,000
6    12,550
7    18,000
7    14,000
9    21,000

a)    Create an appropriate graph that represents the above data.
b)    Find the equation of the regression line. Add this line on your scatterplot.
c)    The y-intercept is__________. In your own words, explain what the y-intercept value represents in this scenario.
d)    The slope is___________. In your own words, explain what the slope represents in this scenario.
e)    A salesman makes a profit of £8,550. Using your regression line, estimate the number of cars the salesman sold. Plot the point on your graph.
f)    Describe the relationship between the number of cars sold and the profit salespeople make.
g)    A salesperson makes £78,000 after selling three cars. Does this fit the trend shown in your graph? Why or why not?

Each sub-question is worth 4 marks, Total 28 marks

2.    Tourists seeking holiday accommodation in a self-catering complex in the resort of Barbados can make either a one or two week booking. The manager of the complex has produced the following table to show the bookings she received last season:

Type of Booking
Tourist's home country    One week    Two week
France    13    44
Germany    29    36
Holland    17    21
Ireland    8    5

Required;
a)    Produce a simple bar chart to show the total number of bookings by home country.
4 marks
b)    Produce a component bar chart to show the number of bookings by home country and type of booking.
4 marks
c)    Produce a clustered bar chart to show the number of bookings by home country and type of booking.
4 marks

3.    Twenty five shoppers were asked about the number of credit cards they carried with them. The table shows the data collected.
Shopper    Number of cards carried
1    2
2    5
3    2
4    0
5    4
6    3
7    0
8    1
9    2
10    7
11    2
12    4
13    1
14    3
15    9
16    4
17    1
18    4
19    1
20    5
21    5
22    2
23    3
24    1
25    2

Required:
a)    Determine the mode and median of this distribution.
4 marks
b)    Calculate the mean of the distribution and compare it to the mode and median. What can you conclude about the shape of the distribution?
6 marks
c)    Draw a bar chart to represent the distribution and confirm your conclusions.
5 marks
d)    Find the lower and upper quartiles of the data and use them to work out the semi-interquartile range.

4.    A garage starts a breakdown service that offers assistance in mornings, afternoons and evenings. The number of call-outs during the first three days of the service are presented in the table below:

Morning    Afternoon    Evening
Day 1    12    6    9
Day 2    15    9    12
Day 3    18    9    15

Required:
a)    Plot the data over time.
4 marks
b)    Work out three-point moving averages for the series and plot them on your graph.
6 marks

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## Assignment Solution

### Problem 1

The sales people at Archway's Car Depot earn commission based on how many and what types of cars they sell. The table below shows the profit y made by ten Archway's Car Depot salespeople after selling x cars.

 Number of cars sold Profit(£) 1 3,500 2 13,000 3 10,000 3 5,700 4 16,500 5 4,000 6 12,550 7 18,000 7 14,000 9 21,000
1. Create an appropriate graph that represents the above data.
2. Find the equation of the regression line. Add this line on your scatterplot.
3. The y-intercept is__________. In your own words, explain what the y-intercept value represents in this scenario.
4. The slope is___________. In your own words, explain what the slope represents in this scenario.
5. A salesman makes a profit of £8,550. Using your regression line, estimate the number of cars the salesman sold. Plot the point on your graph.
6. Describe the relationship between the number of cars sold and the profit salespeople make.

A salesperson makes £78,000 after selling three cars. Does this fit the trend shown in your graph? Why or why not?