Statistical Worksheets

BAR CHARTS

Example 9.1

For this e-portfolio exercise, students were required to partake in various exercises using Excel.

For the first exercise, the instructions were to open an Excel spreadsheet and select the clustered column chart, followed by further instructions for the layout of the chart for Area 1.

The result:

9 1D

It is clear from the chart that Brand A is least preferred, followed by Brand B, whilst the majority of respondents preferred some other brand.

Exercise question:

Add a percentage frequency bar chart showing the brand preferences in Area 2, using the same format as that employed for the Area1 results in the above example. Drag your new chart so that it lies alongside that for Area 1.

Exercise answer:

9 1Da

In this chart, even though figures differ, it is still clear from the chart that Brand A is least preferred, followed by Brand B, whilst the majority of respondents preferred some other brand.

Example 9.2

In this exercise, the same instructions were given as above, however, this time to include both data sets and do a comparison column chart.

The result:

9 1Db

It is clear from the chart that in both Areas, Brand A is least preferred, followed by Brand B, whilst even more respondents preferred some other brand. However, it is now very clear that Brand A and Brand B preferences were both higher in Area 2 than in Area 1, whilst the percentage of respondents who preferred other brands was lower in Area 2.

Exercise question:

Open the Excel workbook in Exa 9.2E.xlsx from the Example folder. This contains the frequency distributions for Data Set E (see the Data Annexe) to which has been added the corresponding percentage frequency distributions. Complete a percentage frequency clustered column bar chart showing the heather species prevalence in the two different locations.

Exercise answer:

9 2E

It is clear from the chart that in location B, the absence was higher than location A, whilst sparse was lower in location B than A. This is followed by abundancy, which was higher in location A than B. Therefore, according to the chart, location A has significantly more frequency.

HISTOGRAMS

Example 9.2

In this exercise, students were to consider dietary data contained in data set B and construct a histogram for the weight losses of those individuals who underwent diet A.

The result:

9 3B

For those individuals who underwent diet A, the weight loss distribution is unimodal and symmetrical, with perhaps a hint of negative skewness.

Exercise 9.3 question:

Open the Excel workbook in Exe 9.3B.xlsx from the Exercises folder. This contains the relative frequency histogram for the Diet A weight loss produced in Example 9.3 together with some of the Diet B weight loss summary statistics. Add a relative frequency histogram of the weight loss for Diet B, where possible using the same classes as those employed for the Diet A results in the above example.

Exercise 9.3 result:

9 3Ba

The histogram for diet B shows a concentration of weight loss around 4 kg, with most participants losing between 2 and 6 kg. The distribution is relatively symmetrical, with no extreme outliers. The highest relative frequency is slightly above 0.4, indicating a strong central tendency. Unlike diet A, there are no instances of weight gain, and the range is more limited, suggesting more consistent results. Overall, diet B appears more predictable, while diet A may offer greater maximum weight loss but with higher variability.

BAR CHARTS

Example 9.4

In this example, students were to produce a percentage frequency for the breakfast cereal brand preferences, based on an excel workbook containing the relevant data.

The result:

9 4 1

It is clear from the chart that Brand A is least preferred, followed by Brand B, whilst most respondents preferred some other brand.

Exercise 9.4 question:

Open the Excel workbook in Exa 9.1D.xlsx from the Exercises folder. This contains the percentage frequencies together with the bar chart just created in the above example. Add a percentage frequency bar chart showing the brand preferences in Area 2, using the same format as that employed for the Area1 results in the above example. Drag your new chart so that it lies alongside that for Area 1.

Exercise 9.4. answer:

9 4 1a

In this chart, even though the data is slightly different, it is still clear from the chart that Brand A is least preferred, followed by Brand B, whilst most respondents preferred some other brand.