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References

Data from The World Bank, available online at http://www.worldbank.org (accessed April 3, 2013).

“Demographics: Obesity – adult prevalence rate.” Indexmundi. Available online at http://www.indexmundi.com/g/r.aspx?t=50&v=2228&l=en (accessed April 3, 2013).

Chapter review

The mean and the median can be calculated to help you find the "center" of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occuring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data, but if your data set consists of ranges which lack specific values, the mean may seem impossible to calculate. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. Multiply each midpoint by the number of values found in the corresponding range. Divide the sum of these values by the total number of data values in the set.

Formula review

μ = f m f Where f = interval frequencies and m = interval midpoints.

Practice

Find the mean for the following frequency tables.

  1. Grade Frequency
    49.5–59.5 2
    59.5–69.5 3
    69.5–79.5 8
    79.5–89.5 12
    89.5–99.5 5
  2. Daily Low Temperature Frequency
    49.5–59.5 53
    59.5–69.5 32
    69.5–79.5 15
    79.5–89.5 1
    89.5–99.5 0
  3. Points per Game Frequency
    49.5–59.5 14
    59.5–69.5 32
    69.5–79.5 15
    79.5–89.5 23
    89.5–99.5 2

Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest:

  • 16
  • 17
  • 19
  • 20
  • 20
  • 21
  • 23
  • 24
  • 25
  • 25
  • 25
  • 26
  • 26
  • 27
  • 27
  • 27
  • 28
  • 29
  • 30
  • 32
  • 33
  • 33
  • 34
  • 35
  • 37
  • 39
  • 40

Calculate the mean.

Mean: 16 + 17 + 19 + 20 + 20 + 21 + 23 + 24 + 25 + 25 + 25 + 26 + 26 + 27 + 27 + 27 + 28 + 29 + 30 + 32 + 33 + 33 + 34 + 35 + 37 + 39 + 40 = 738;

738 27 = 27.33

Identify the median.

Identify the mode.

The most frequent lengths are 25 and 27, which occur three times. Mode = 25, 27


Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:

sample mean = x = _______

median = _______

4

mode = _______

Bringing it together

Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed 100 shoppers. The samples yielded the following information.

Javier Ercilia
x 6.0 miles 6.0 miles
s 4.0 miles 7.0 miles
  1. How can you determine which survey was correct ?
  2. Explain what the difference in the results of the surveys implies about the data.
  3. If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? How do you know?
    This shows two histograms. The first histogram shows a fairly symmetrical distribution with a mode of 6. The second histogram shows a uniform distribution.
  4. If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilia’s sample? How do you know?
    This shows two horizontal boxplots. The first boxplot is graphed over a number line from 0 to 21. The first whisker extends from 0 to 1. The box begins at the first quartile, 1, and ends at the third quartile, 14. A vertical, dashed line marks the median at 6. The second whisker extends from the third quartile to the largest value, 21. The second boxplot is graphed over a number line from 0 to 12.  The first whisker extends from 0 to 4. The box begins at the first quartile, 4, and ends at the third quartile, 9. A vertical, dashed line marks the median at 6. The second whisker extends from the third quartile to the largest value, 12.

Use the following information to answer the next three exercises : We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.

Number of years Frequency Number of years Frequency
Total = 20
7 1 22 1
14 3 23 1
15 1 26 1
18 1 40 2
19 4 42 2
20 3

What is the IQR ?

  1. 8
  2. 11
  3. 15
  4. 35

a

What is the mode?

  1. 19
  2. 19.5
  3. 14 and 20
  4. 22.65

Is this a sample or the entire population?

  1. sample
  2. entire population
  3. neither

b

Questions & Answers

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a regulatory object between producer and consumer of monetary system
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money is anything generally accepted for the payment of goods and services and for the settlement of debt
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a regulatory object of good and services between producer and consumer ( all these comes under monetary system)
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flexibility of demand in terms of price , income and tax ratio .
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economic growth, establishment of industry, encourage of investor's, farm productivities, creation of institutions, construction of good road etc
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elasticity of demand can be said to be the responsiveness of demand to a change in prices
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Economic is the study of scarcity
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Economics is the study of a lot of things. It is split up into two areas of study, Microeconomics and Macroeconomics. Microeconomics is the study of an individual's choices in the economy and Macroeconomics is the study of the economy as a whole.
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Source:  OpenStax, Statistics i - math1020 - red river college - version 2015 revision a - draft 2015-10-24. OpenStax CNX. Oct 24, 2015 Download for free at http://legacy.cnx.org/content/col11891/1.8
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