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Statistics: misuse of statistics

Module by: Free High School Science Texts Project. E-mail the author

Misuse of Statistics

Statistics can be manipulated in many ways that can be misleading. Graphs need to be carefully analysed and questions must always be asked about 'the story behind the figures.' Potential manipulations are:

  1. Changing the scale to change the appearence of a graph
  2. Omissions and biased selection of data
  3. Focus on particular research questions
  4. Selection of groups

Investigation : Misuse of statistics

  1. Examine the following graphs and comment on the effects of changing scale.
    Figure 1
    Figure 1 (MG11C18_008.png)
    Figure 2
    Figure 2 (MG11C18_009.png)
  2. Examine the following three plots and comment on omission, selection and bias. Hint: What is wrong with the data and what is missing from the bar and pie charts?
    Table 1
    ActivityHours
    Sleep8
    Sports2
    School7
    Visit friend1
    Watch TV2
    Studying3
    Figure 3
    Figure 3 (MG11C18_010.png)
    Figure 4
    Figure 4 (MG11C18_011.png)

Misuse of Statistics

The bar graph below shows the results of a study that looked at the cost of food compared to the income of a household in 1994.

Figure 5
Figure 5 (MG11C18_012.png)

Table 2
Income (thousands of rands) Food bill (thousands of rands)
<<5 2
5-10 2
10-15 4
15-20 4
20-30 8
30-40 6
40-50 10
>>50 12
  1. What is the dependent variable? Why?
  2. What conclusion can you make about this variable? Why? Does this make sense?
  3. What would happen if the graph was changed from food bill in thousands of rands to percentage of income?
  4. Construct this bar graph using a table. What conclusions can be drawn?
  5. Why do the two graphs differ despite showing the same information?
  6. What else is observed? Does this affect the fairness of the results?

End of Chapter Exercises

  1. Many accidents occur during the holidays between Durban and Johannesburg. A study was done to see if speeding was a factor in the high accident rate. Use the results given to answer the following questions.
    Table 3
    Speed (km/h)Frequency
    60<x≤7060<x≤703
    70<x≤8070<x≤802
    80<x≤9080<x≤906
    90<x≤10090<x≤10040
    100<x≤110100<x≤11050
    110<x≤120110<x≤12030
    120<x≤130120<x≤13015
    130<x≤140130<x≤14012
    140<x≤150140<x≤1503
    150<x≤160150<x≤1602
    1. Draw a graph to illustrate this information.
    2. Use your graph to find the median speed and the interquartile range.
    3. What percent of cars travel more than 120km.h-1120km.h-1 on this road?
    4. Do cars generally exceed the speed limit?
  2. The following two diagrams (showing two schools contribution to charity) have been exaggerated. Explain how they are misleading and redraw them so that they are not misleading.
    Figure 6
    Figure 6 (MG11C18_013.png)
  3. The monthly income of eight teachers are given as follows: R10 050; R14 300; R9 800; R15 000; R12 140; R13 800; R11 990; R12 900.
    1. What is the mean income and the standard deviation?
    2. How many of the salaries are within one standard deviation of the mean?
    3. If each teacher gets a bonus of R500 added to their pay what is the new mean and standard deviation?
    4. If each teacher gets a bonus of 10% on their salary what is the new mean and standard deviation?
    5. Determine for both of the above, how many salaries are within one standard deviation of the mean.
    6. Using the above information work out which bonus is more beneficial financially for the teachers.

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