Statistics Assignment: Statistical Data Analysis and Sales Forecasting

This statistics assignment solution provides a comprehensive analysis of a given dataset, covering descriptive statistics such as mean, standard deviation, median, quartiles, minimum, and maximum values. It includes data grouping, histogram construction, and ogive creation for visual representation. The assignment also explores the differences between raw data mean and grouped data mean, explains nominal and ordinal data, and differentiates between mean and median. Furthermore, it delves into sales forecasting using an additive model, computes average seasonal variations, and provides final forecasts for the year 2019, discussing factors such as customer purchasing power and pricing that could affect the forecast. Desklib provides a platform for students to access similar solved assignments and past papers.

Statistics Assignment
Student’s Name
Institution Affiliation

Part 1
1. Computation of the mean, standard deviation, median, Q1 and Q3, min and max for the
data.
The results are indicated in the table below
Mean 9.60
Standard Deviation 3.04
Median 9.40
Q1 7.00
Q3 12.54
Maximum 14.63
Minimum 3.59
2. Group the data
Spend per customer in Café
£
Frequency(f
)
3-6 5
6-9 16
9-12 15
12-15 14

3. Using this Grouped data to:
i. Compute mean
Spend per customer in
Café £
Frequency(f) Mid-point(x) f*x
3-6 5 4.5 22.5
6-9 16 7.5 120
9-12 15 10.5 157.5
12-15 14 13.5 189
Sum 50 489
Mean=∑ f ∗x
∑ f
9.78
ii. Construction histogram
3-6 6-9 9-12 12-15
0
2
4
6
8
10
12
14
16
18
Histogram of Spend per customer in Café £
Spend per customer in Café £
Frequency

iii. Draw the Ogive
2 4 6 8 10 12 14 16
0
10
20
30
40
50
60
Ogive
Spend per customer in Café £
Cumulative Frequency
Reading from the Ogive for the median and Q1 and Q3
Q1 7.1
Q2 9.5
Q3 12.5
Part 2
1. why the raw data mean and grouped data mean are different
Raw data mean (9.60) is a central representative value of data, whereas grouped data mean
(9.78) is an estimate of the central value. The manager should go for the raw data mean
(9.60) as it will give the actual central representative value of the data.

2. Explaining the meaning of terms
 Nominal data
Are a set of observations that can be labeled using numbers. The observations are countable
but cannot be ordered or ranked for example the Sex of the customer using the Airport Café.
 Ordinal data
These are observations that can be ranked or ordered. They a rating scale. Observations are
countable, can be ordered but have no measure, for example, the level of spending of
customers using the airport café.
3. Difference between mean and median
Mean is the arithmetic average of the data; used to measure the central representative value of
the data, whereas median is the middle term of a set of data that separates the higher half of the
data and from the lower half.

Part 3
1. Model of choice
Additive model, which is represented by y=t+s, where :
y=sales value at a given time point ,
t=Moving avearge trend
s=seasonal Variation factor
Below is a graph to show this
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
2015 2016 2017 20
18
0
10
20
30
40
50
60
70
80
Sales(000's) y
Trend (t)
Seasonally adjusted
values y-s
2. Average seasonal Variation Computation
The following table shows the results of the computation of Average seasonal variation.

Year Quarter Sales(000's) y
Trend
(t) y-t S y-s
2015 Q1 3 -20.985 23.985
Q2 22 1.078 20.922
Q3 45 19.45 25.55 34.142 10.858
Q4 6 19.875 -13.875 -14.235 20.235
2016 Q1 5 22.25 -17.25 -20.985 25.985
Q2 25 25 0 1.078 23.922
Q3 61 26.125 34.875 34.142 26.858
Q4 12 27.125 -15.125 -14.235 26.235
2017 Q1 8 29.5 -21.5 -20.985 28.985
Q2 30 31.875 -1.875 1.078 28.922
Q3 75 33 42 34.142 40.858
Q4 17 36.75 -19.75 -14.235 31.235
2018 Q1 12 42.25 -30.25 -20.985 32.985
Q2 56
Q3 93
Seasonal variation Computation
Q1 Q2 Q3 Q4 Sum
2015 25.55 -13.875
2016 -17.25 0 34.875 -15.125
2017 -21.5 -1.875 42 -19.75
2018 -30.25
Total(sum) -69 -1.875 102.425 -48.75 -17.2
Average -23 -0.938 34.142 -16.250 -6.046
adjustment +2.015 +2.015 0.000 +2.015 +6.046
Adjusted
average -20.985 1.078 34.142 -14.235 0.000
Notes
The adjusted average value is the Average Seasonal Variation (ASV), computed by:
ASV = Average+ adjustment

Average=∑ of ( y−t )÷number of years
3. Final Forecasts for the year 2019
The sales forecast and trend values are shown in the table below.
The sales forecast were computed using the additive model, using the forecasted trend values
for the year 2019.
Forcasted Trend ( t )=2018Q4 Trend Value+n∗( Averaage change per quarter ) , whre , n=number of quarters
Averaage change per quarter= Range of trend values
number of trend value ( n ) −1
Forecasted sales value=Forcasted Trend +Average Seasonal variation
Year Quarter Forecasted sales value Forecasted trend Average Seasonal variation
2019 Q1 28.105 49.09 -20.985
Q2 52.448 51.37 1.078
Q3 87.792 53.65 34.142
Q4 41.695 55.93 -14.235
4. Discussion of factors affecting the forecast
i. Customer purchasing power: This customer’s ability to buy products from the airport
café, this determines by the amount of disposable income they hold at a given period in
time. This normally causing fluctuation of sales trend, when high the trend will rise and
when low the trend will fall

ii. Pricing of the Café’s produce: This affects customers’ buying habits hence rising and
falling of sales made. Consequently, there will be a high variation of sales with time
iii. The error made during the computation of forecasts affects the reliability of the
forecasted values