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Measures of Central Tendency and Dot Plots. Refreshing Your Skills – Chapter 2. Values called measures of central tendency are used to summarize data into a single value or statistic. The mean is the sum of all the data values divided by the number of values.

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measures of central tendency and dot plots

Measures of CentralTendency and Dot Plots

Refreshing Your Skills – Chapter 2

slide2

Values called measures of central tendency are used to summarize data into a single value or statistic.

    • The mean is the sum of all the data values divided by the number of values.
    • The median is the middle number when the data are arranged in order.
    • The mode is the value that occurs most frequently in the data.
example a
Example A
  • Find the three measures of central tendency for these backpack weights (in pounds):

10, 20, 9, 17, 3, 10, 15, 15, 7, 10, 9, 10, 9, 7, 4, 6, 7, 9, 13, 10, 8, 7, 4, 4, 8, 33, 10, 9, 7, 16

The sum of all 30 values is 306. When you divide by 30, you find 10.2 lb is the mean.

example a1
Example A
  • Find the three measures of central tendency for these backpack weights (in pounds):

10, 20, 9, 17, 3, 10, 15, 15, 7, 10, 9, 10, 9, 7, 4, 6, 7, 9, 13, 10, 8, 7, 4, 4, 8, 33, 10, 9, 7, 16

The median is 9 lb, the middle value when the data are arranged in order.

example a2
Example A
  • Find the three measures of central tendency for these backpack weights (in pounds):

10, 20, 9, 17, 3, 10, 15, 15, 7, 10, 9, 10, 9, 7, 4, 6, 7, 9, 13, 10, 8, 7, 4, 4, 8, 33, 10, 9, 7, 16

The mode is 10 lb, the weight that occurs most frequently.

slide6

You can justify using any of these three statistics as a typical weight.

  • If you wanted to present a statistic that implies backpacks are too heavy, you might use the mean because it is higher than the median or mode due to one very large data value.
  • When a data set has one or more values that are far from the rest, the median often is more representative of the data than the mean.
slide7

A dot plot is a statistical graph in which each value in the sample is plotted above a number line. The dot plot for backpack data looks like this.

If you have a dot plot of a data set, you can find the median or the mode by counting the dots and noting their position.

example b
Example B
  • Use the dot plot to find the three measures of central tendency for this sample.

There are seven data values, so the fourth data value is the median. Counting in four values from either end, the median is 65 in.

The mean is

The mode is 65 in., the height that occurs most frequently.

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