Measures of Central Tendency and Dispersion

1
Measures of Central Tendency and Dispersion

• MM1D4 Students will explore variability of data
  by determining the mean absolute deviation (The
  average of the absolute values of the deviations).

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Mean

• Average
• ____
• X
• Ex Find the mean 2, 4, 37, 24, 18, 10
• ADD 2 4 37 24 18 10 95
• Divide 95/6
• 15.83

3
Median

• Middle number when the values are written in
  numerical order.
• Ex1 3, 1, 35, 4, 22
• Put in order 1, 3, 4, 22, 35
• Locate middle number 1, 3, 4, 22, 35
• Ex Find the median 2, 4, 37, 24, 18, 10
• Put in order 2, 4, 10, 18, 24, 37
• Locate middle number 2, 4, 10, 18, 24, 37
• If Two then average (10 18)/2

4
Mode

• The value that occurs most frequently
• There may be no mode, one mode, or more than one
  mode.
• Ex 2, 6, 1, 21, 1, 33, 42

5
Range

• The difference of the greatest value and the
  least value
• Ex Find the range 3, 1, 35, 4, 22
• 35 1

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standard deviation

• standard deviation a statistic that tells you
  how tightly all the various examples are
  clustered around the mean in a set of data.
• When the examples are pretty tightly bunched
  together and the bell-shaped curve is steep, the
  standard deviation is small.
• When the examples are spread apart and the bell
  curve is relatively flat, that tells you have a
  relatively large standard deviation

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Standard Deviation Example

• To find the Standard deviation of 1,2,3,4,5.
• Step 1 Calculate the mean and deviation.

list Mean ( - m) ( - m)2
1
2
3
4
5
of items Sum
8
list Mean ( - m) ( - m)2
1 3 -2 4
2 3 -1 1
3 3 0 0
4 3 1 1
5 3 2 4
of items 5 Sum 10

• Step 2 n 5, the total number of items. Find
  n-1.
•             5-1 4
•   Step 3Now find Standard Deviation using the
  formula. v(sum of squares/ n-1)
•             v10/v4 1.58113