# 9.3 Misuse of statistics

 Page 1 / 1

## 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.
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.

## Summary of definitions

• The mean of a data set, $x$ , denoted by $\overline{x}$ , is the average of the data values, and is calculated as:
$\overline{x}=\frac{\mathrm{sum}\mathrm{of}\mathrm{values}}{\mathrm{number}\mathrm{of}\mathrm{values}}$
• 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.
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.
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.
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 $45,0\le m<50,0$ $50,0\le m<55,0$ $55,0\le m<60,0$ $60,0\le m<65,0$ $65,0\le m<70,0$ $70,0\le m<75,0$ $75,0\le m<80,0$
2. Draw a frequency polygon for this information.
3. What can you conclude from looking at the graph?
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.
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)?
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?
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.
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?
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 =

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!