<< Chapter < Page Chapter >> Page >

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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 10 maths [ncs]' conversation and receive update notifications?

Ask