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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.
  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.
  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?
  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

End of chapter summary

  • Data types can be divided into primary and secondary data. Primary data may be further divided into qualitative and quantitative data.
  • We use the following as measures of central tendency:
    • 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 are measures of dispersion:
    • The range of a data set is the difference between the lowest value and the highest value in the set.
    • Quartiles are the three data values that divide an ordered data set into four groups containing equal numbers of data values. The median is the second quartile.
    • Percentiles are the 99 data values that divide a data set into 100 groups.
    • The inter quartile range is a measure which provides information about the spread of a data set, and is calculated by subtracting the first quartile from the third quartile, giving the range of the middle half of the data set, trimming off the lowest and highest quarters, i.e. Q 3 - Q 1 . Half of this value is the semi-interquartile range.
  • The five number summary is a way to summarise data. A box and whisker plot is a graphical representation of the five number summary.
  • Random errors are found in all sets of data and arise from estimating data values. Bias or systematic error occurs when you consistently under or over estimate data values.
  • You must always consider the data and the statistics that summarise the data

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, 6, 7, 5, 4, 6, 6, 6, 7, 4. Find the mode of their ages.
  4. 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.
  5. 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)?
  6. 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?
  7. 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.
  8. 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?
  9. 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 =

Questions & Answers

What is inflation
Bright Reply
a general and ongoing rise in the level of prices in an economy
AI-Robot
What are the factors that affect demand for a commodity
Florence Reply
price
Kenu
differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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