T3 2019 Holmes Institute HA1011 Group Assignment Statistical Analysis

This assignment solution addresses a group project from the HA1011 Applied Quantitative Methods course, focusing on statistical analysis and data interpretation. The solution begins by differentiating between population and sample data, explaining how the provided data is a sample. It calculates the population mean and standard deviation, then determines the Interquartile Range (IQR) to describe data spread. The solution then performs a regression analysis to explore the relationship between annual sales and advertising expenditure, including the creation of a table with relevant calculations, and interpretation of the correlation between the two variables. The assignment demonstrates understanding of statistical principles, techniques, and their application in business research.

a. A collection of population data includes all members of a given group. On the other hand, a
sample is a dataset that contains a part or subset of population. Here the data is a sample where
the manager had picked only 12 products from all on random basis. All statistical operations will
be implemented on this sample only and the conclusion will be applied to the entire population.
b. Calculate population mean:
Calculate standard deviation:
c. Find IQR:
1. Apply sorting.
20 20 30 30 30 40 60 60 60 70 90 100
2. Calculate the median.

3. Find upper and lower median .
Lower median:
20 20 30 30 30 40
Upper median:
60 60 60 70 90 100
4. Calculate IQR:
The IQR (35) is the better choice for explaining spread’s amount in the middle half of the data
that year as it is not affected by the outliers.
d. Let:
Annual sales = x
Annual advertising expenditure = y
Make table:
Produ
ct
Annual Sales
($1000) (x)
Annual Advertising
Expenditures ($1000)(y) xy x^2 y^2
1 150 60 9000 22500 3600
2 150 60 9000 22500 3600
3 190 100 1900 36100 1000

0 0
4 130 30 3900 16900 900
5 120 20 2400 14400 400
6 110 20 2200 12100 400
7 160 30 4800 25600 900
8 180 70
1260
0 32400 4900
9 180 90
1620
0 32400 8100
10 150 40 6000 22500 1600
11 160 30 4800 25600 900
12 140 60 8400 19600 3600
Sum 1820.00 610
9830
0
28260
0
3890
0
Substitute the values:
There is a strong relationship between both variables.