Chapter 3 Review MDM 4U

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Chapter 3 ReviewMDM 4U

• Gary Greer

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3.1 Graphical Displays

• be able to effectively use a histogram
• recognize and be able to interpret the various
  types of distributions
• ex when would we use a histogram vs. a bar
  graph?
• ex how do you calculate bin width?

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3.2 Central Tendency

• be able to calculate mean, median, mode and
  weighted mean
• ex determine which measure is appropriate
• be aware of the effect of outliers
• recognize the location of the measures with
  respect to skewed distributions
• if mean gt medianright skew
• if mean lt medianleft skew

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3.3 Measures of Spread

• be able to calculate IQR and population standard
  deviation
• interpret the meaning of the values
• the larger the standard deviation, the larger the
  spread of data
• IQR gives the range containing 50 of the data
• what is the population standard deviation for
• 3 5 7 8 8 9 10 12 14
• ans 3.166

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3.4 Normal Distribution

• be familiar with the characteristics of a normal
  distribution
• use a normal distribution to calculate the ranges
  of expected data
• ex with a mean of 10 and a standard deviation of
  2, how many percent of the data lie between 6 and
  14?
• ans 95, with a std dev of 2, 6 is 2 std dev
  below the mean and 14 us 2 above. So 95 of the
  data falls in the range (see diagram)

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Normal Distribution
99.7
95
68
34
34
0.15
0.15
13.5
13.5
2.35
2.35
x
x 1s
x 2s
x 3s
x - 1s
x - 2s
x - 3s
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3.5 Z-Scores

• understand the use of the standard normal
  distribution
• be able to calculate a z-score
• be able to calculate the percentile position of a
  piece of data, given the standard deviation and
  the mean
• be able to calculate the percent of data in a
  range of population values

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3.5 Z-Scores

• ex given a normal distribution with a mean of 10
  and a std dev of 2, what percent of the
  population is between 7 and 11?
• ans calculate z-scores for the two data values
  and subtract their percentile positions
• for 7 (7 10)/2 -1.5 z 6.68
• for 11 (11-10)/2 0.5 z 69.15
• 69.15-6.68 62.47
• so 62.47 lies between these two values

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3.6 Mathematical Indices

• these are arbitrary numbers that provide a
  measure of something
• students should be able to work with a given
  formula and interpret the meaning of calculated
  results