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Misuse of statistics

In many cases groups can gain an advantage by misleading people with the misuse of statistics.

Common techniques used include:

  • Three dimensional graphs.
  • Axes that do not start at zero.
  • Axes without scales.
  • Graphic images that convey a negative or positive mood.
  • Assumption that a correlation shows a necessary causality.
  • Using statistics that are not truly representative of the entire population.
  • Using misconceptions of mathematical concepts

For example, the following pairs of graphs show identical information but look very different. Explain why.

Exercises - misuse of statistics

  1. A company has tried to give a visual representation of the increase in their earnings from one year to the next. Does the graph below convince you? Critically analyse the graph.
    Click here for the solution
  2. In a study conducted on a busy highway, data was collected about drivers breaking the speed limit and the colour of the car they were driving. The data were collected during a 20 minute time interval during the middle of the day, and are presented in a table and pie chart below.
    • Conclusions made by a novice based on the data are summarised as follows:
    • “People driving white cars are more likely to break the speed limit.”
    • “Drivers in blue and red cars are more likely to stick to the speed limit.”
    • Do you agree with these conclusions? Explain.
    Click here for the solution
  3. A record label produces a graphic, showing their advantage in sales over their competitors. Identify at least three devices they have used to influence and mislead the readers impression.
    Click here for the solution
  4. In an effort to discredit their competition, a tour bus company prints the graph shown below. Their claim is that the competitor is losing business. Can you think of a better explanation?
    Click here for the solution
  5. To test a theory, 8 different offices were monitored for noise levels and productivity of the employees in the office. The results are graphed below.
    The following statement was then made: “If an office environment is noisy, this leads to poor productivity.”Explain the flaws in this thinking.
    Click here for the solution

Summary of definitions

  • The mean of a data set, x , denoted by x ¯ , is the average of the data values, and is calculated as:
    x ¯ = sum of values number of values
  • The median is the centre data value in a data set that has been ordered from lowest to highest
  • The mode is the data value that occurs most often in a data set.

The following presentation summarises what you have learnt in this chapter. Ignore the chapter number and any exercise numbers in the presentation.

Summary

  • Data types
  • Collecting data
  • Samples and populations
  • Grouping data TallyFrequency bins
  • Graphing data Bar and compound bar graphsHistograms and frequency polygons Pie chartsLine and broken line graphs
  • Summarising data
  • Central tendency MeanMedian ModeDispersion RangeQuartiles Inter-quartile rangePercentiles
  • Misuse of stats

Exercises

  1. Calculate the mean, median, and mode of Data Set 3.
    Click here for the solution
  2. The tallest 7 trees in a park have heights in metres of 41, 60, 47, 42, 44, 42, and 47. Find the median of their heights.
    Click here for the solution
  3. The students in Bjorn's class have the following ages: 5, 9, 1, 3, 4, 6, 6, 6, 7, 3. Find the mode of their ages.
    Click here for the solution
  4. The masses (in kg, correct to the nearest 0,1 kg) of thirty people were measured as follows:
    45,1 57,9 67,9 57,4 50,7 61,1 63,9 67,5 69,7 71,7
    68,0 63,2 58,7 56,9 78,5 59,7 54,4 66,4 51,6 47,7
    70,9 54,8 59,1 60,3 60,1 52,6 74,9 72,1 49,5 49,8
    1. Copy the frequency table below, and complete it.
      Mass (in kg) Tally Number of people
      45 , 0 m < 50 , 0
      50 , 0 m < 55 , 0
      55 , 0 m < 60 , 0
      60 , 0 m < 65 , 0
      65 , 0 m < 70 , 0
      70 , 0 m < 75 , 0
      75 , 0 m < 80 , 0
    2. Draw a frequency polygon for this information.
    3. What can you conclude from looking at the graph?
    Click here for the solution
  5. An engineering company has designed two different types of engines for motorbikes. The two different motorbikes are tested for the time it takes (in seconds) for them to accelerate from 0 km/h to 60 km/h.
    Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 Test 10 Average
    Bike 1 1.55 1.00 0.92 0.80 1.49 0.71 1.06 0.68 0.87 1.09
    Bike 2 0.9 1.0 1.1 1.0 1.0 0.9 0.9 1.0 0.9 1.1
    1. What measure of central tendency should be used for this information?
    2. Calculate the average you chose in the previous question for each motorbike.
    3. Which motorbike would you choose based on this information? Take note of accuracy of the numbers from each set of tests.
    Click here for the solution
  6. The heights of 40 learners are given below.
    154 140 145 159 150 132 149 150 138 152
    141 132 169 173 139 161 163 156 157 171
    168 166 151 152 132 142 170 162 146 152
    142 150 161 138 170 131 145 146 147 160
    1. Set up a frequency table using 6 intervals.
    2. Calculate the approximate mean.
    3. Determine the mode.
    4. How many learners are taller than your approximate average in (b)?
    Click here for the solution
  7. In a traffic survey, a random sample of 50 motorists were asked the distance they drove to work daily. This information is shown in the table below.
    Distance in km 1-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45
    Frequency 4 5 9 10 7 8 3 2 2
    1. Find the approximate mean.
    2. What percentage of samples drove
      1. less than 16 km?
      2. more than 30 km?
      3. between 16 km and 30 km daily?
    Click here for the solution
  8. A company wanted to evaluate the training programme in its factory. They gave the same task to trained and untrained employees and timed each one in seconds.
    Trained 121 137 131 135 130
    128 130 126 132 127
    129 120 118 125 134
    Untrained 135 142 126 148 145
    156 152 153 149 145
    144 134 139 140 142
    1. Find the medians and quartiles for both sets of data.
    2. Find the Interquartile Range for both sets of data.
    3. Comment on the results.
    Click here for the solution
  9. A small firm employs nine people. The annual salaries of the employers are:
    R600 000 R250 000 R200 000
    R120 000 R100 000 R100 000
    R100 000 R90 000 R80 000
    1. Find the mean of these salaries.
    2. Find the mode.
    3. Find the median.
    4. Of these three figures, which would you use for negotiating salary increases if you were a trade union official? Why?
    Click here for the solution
  10. The marks for a particular class test are listed here:
    67 58 91 67 58 82 71 51 60 84
    31 67 96 64 78 71 87 78 89 38
    69 62 60 73 60 87 71 49

    Complete the frequency table using the given class intervals.

    Class Tally Frequency Mid-point Freq × Midpt
    30-39 34,5
    40-49 44,5
    50-59
    60-69
    70-79
    80-89
    90-99
    Sum = Sum =

    Click here for the solution

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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