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  • Evan John Evan John
  • 7 min read

Descriptive Statistics and Data Distribution

 

Assignment Requirement
Introduction

 

Learning Outcomes

LO (3) Use statistical techniques for data analysis and visualization.

LO (4) Evaluate statistical results.

LO (5) Use statistical software for data analysis and visualization.

 

Formatting guidelines:

Please use:

 

✔      Times New Roman

✔      Size 14 text.

✔      1.5 line spacing

✔      Bold headings

✔      Align paragraph: Justify.

 

Please include:

 

✔      Your word count at the cover page of the report, written in brackets – e.g. (Words: 2021)

✔      Citations in the text (Roger et al. 2022) or (Daubman and Lehman, 1993)

✔      A reference list showing all cited sources in alphabetical order (e.g., start with A, then B, then C and so on)

✔      Use Harvard style.

 

Please see “Referencing Guide” on the Academic Practice Learning Central page for examples.

 

Sections to include:

The exercise needs to have the following sections:

 

✔      Title

✔      Problem

✔      Methods and discussion

✔      Conclusion

✔      References (2 reference for each problem)

 

Title

✔      Every exercise needs a title.

✔      The title should be short and informative.

✔      A title such as “The statistical analysis of central and dispersion measures of data sets” are informative and, as such, totally acceptable.

 

 

Introduction (Problem)

✔      This should describe the problem to solve, including a general description of available data. In this case, you need to put or add the exercise text, including the data available.

 

Methods

✔      These should now be described in a fair amount of detail, including any theory necessary to solve the problem. Aim to write for someone of comparable standing, e.g., a student in the same year as yourself, who does not know anything about the report’s subject. Don’t be afraid of putting very detailed and long descriptions.

 

✔      It should describe in detail the precise statistical tools and techniques to be used and reveal the way you lead to the desired results (e.g. mean, standard deviation, regression). Do not shy away from using mathematical notation (get well familiar with the capabilities of your word-processor to produce mathematical expressions) but be careful to define every bit of the notation you use.

 

✔      In this section is important that you describe your analysis clearly and carefully to enable it to be reproduced by the reader.

 

✔      For each statistical tool and technique, you need to describe what it is, its aim and how to obtain it (mathematical equation). Plots are part of the techniques and need to be explained (what is and aim).

 

Results and discussion

 

✔      In this section, you must include all tables (Values, results) and graphs indicated in each exercise.

✔      You need to discuss each value, diagram, and plot.

✔      Tables, figures, graphs, and diagrams should be titled and numbered with a caption.

✔      Tables need titles, numbering, and captions.

✔      All the plots need to contain the elements indicated in Table 1 (end of this document)

✔      Your discussion needs to contain references.

 

Conclusion

✔      Your conclusions should be expressed in a way that can be understood by a non-statistician and should make sense.

 

References

✔      These should always be included if you refer to books or papers from journals.

✔      Citations in the text (Roger et al. 2022)

✔      A reference list showing all cited sources in alphabetical order (e.g., start with A, then B, then C and so on)

✔      Use Harvard style.

✔      You only need one reference section, including references used in the five exercises.

 

 

 

Task 1: Descriptive Statistics and Data Distribution

You are an analyst for a publicly traded company. The controller wants to analyse how many days it takes to complete the month-end financial close process. The goal is to close within 5 business days.

16 21 35 42 28 33 47 19 26 39
25 24 18 26 52 36 29 40 22 48
16 27 38 45 50 34 23 41 30 37
20 24 46 54 49 25 17 43 51 55
15 28 39 47 53 26 34 42 31 44

 

  1. a) Construct a frequency distribution table using 6 classes.
  2. b) Use Excel to construct a histogram. Interpret the results.
  3. c) Calculate the mean for ungroup data.
  4. d) Calculate the median for ungroup data.
  5. e) Calculate the variance for ungroup data
  6. f) Calculate the standard deviation for ungroup data.
  7. g) Calculate the mean for group data.
  8. h) Calculate the median for group data.
  9. i) Calculate the variance for group data.
  10. j) Calculate the standard deviation for group data.
  11. k) Compare the result for the ungroup and group data for the mean, median, variance and standard deviation.

 

 

 

Structure for task 1

1- Write down the introduction

2- Main body

3- Conclusion

4- Two references

****************************************************************

Task 2: Correlation and Linear Regression

You are a junior analyst at a retail analytics firm that supports data-driven decisions for client companies. One of your clients, a national retail chain, is reviewing the performance of 13 of their key products. They have provided you with data showing the number of units sold for each product and the corresponding profit per unit (in £).

Your task is to examine this data and help the company understand whether there is a pattern or relationship between how many units are sold and how profitable each unit is.

Unit 4 20 12 11 8 6 20 2 7 24 27 3 8
Profit 120 200 140 120 120 122 190 100 120 190 190 110 120

 

  1. a) Using excel to produce a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between the unit and the profit?
  2. b) Find the regression equation of the number of profit on the unit.
  3. c) Give a brief interpretation of the values of and calculated in part b.
  4. d) Calculate the profit with 16 unit.
  5. e) Compute the standard deviation of errors .
  6. f) Compute the coefficient of determination and give a brief interpretation of it.
  7. g) Calculate the correlation between unit and the profit and give a brief interpretation of it.

Structure for task 2

1- Write down the introduction

2- Main body

3- Conclusion

4- Two references

 

****************************************************************

Task 3: Hypothesis Testing

  1. a) A pharmaceutical company is evaluating the performance of a new productivity-enhancing supplement designed for office employees. The company claims the supplement does not adversely affect employees’ overall well-being. One important health metric monitored by HR and occupational health teams is the white blood cell (WBC) count, which can be an indicator of immune system balance. In healthy adults, the average WBC count is known to be approximately 7.5 × 10³ cells per millilitre. To investigate whether the new supplement causes any significant change in WBC levels, a random sample of employees currently taking the supplement was selected, and their WBC counts were measured.

The following results (in 10³ cells/ml) were recorded:

 

6.50    8.69    6.85    6.76    6.58    8.84    8.44    8.28    7.65    6.95    10.12

8.74    8.00    8.84    7.93    7.65    7.00    6.70    9.20    6.45    7.66

 

Assume the distribution of white blood cell counts is normal and . Conduct a hypothesis test to determine whether there is any change in the mean white blood cell count due to the arthritis drug. Use .

 

 

  1. b) Kennebunk Port, Maine, is a well-known coastal town that thrives on tourism. However, during the winter months particularly in January local businesses experience a sharp decline in hotel bookings. On average, hotel room occupancy rates during the winter season have historically been around 23.1%, indicating limited tourist activity.

To address this issue, the town’s business council launched a new digital advertising campaign aimed at increasing winter tourism. After the campaign was implemented, hotel managers collected data over a sample of nine winter days, recording the daily room occupancy rates.

The sample revealed a mean occupancy rate of 24.1% with a standard deviation of 1.8%.

You have been asked to evaluate whether the campaign has led to a statistically significant increase in hotel room occupancy during the winter season. Using the data provided, conduct a hypothesis test at the 1% significance level (α = 0.01). Assume the population distribution of occupancy rates is normal.

If the test is significant, can you conclude that the advertising campaign was effective in increasing winter hotel bookings?

 

Structure for task 3

1- Write down the introduction for both parts

2- Main body

3- Conclusion for both parts

4- Two references

Assignment

 

The Concise Guide to the Technical and Structural Specifications for the Preparation of Academic Theses

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