MATH 1107 Elementary Statistics

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MATH 1107Elementary Statistics

• Lecture 5
• The Standard Deviation
• as a Ruler

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MATH 1107 Using the STD DEV for Relative
Standing

Following from the example in your book (page
100)is it a more impressive performance to win
the 800 meters by 8 seconds or the long jump by
60 cm? Was Babe Ruth a better hitter than Barry
Bonds?
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MATH 1107 Using the STD DEV for Relative
Standing
The only way to compare values in different units
is to standardize the deviations from the means.
In other words, we first have to convert all of
the values into similar units standard
deviations from the respective means. THEN, we
can compare them directly. This is done through
the application of a Z-score
Value of interest
Mean of data
Std dev of data
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MATH 1107 Using the STD DEV for Relative
Standing
Continuing with the example in the book (page
101)
The winning 800m time of 129 second was 8 seconds
better than the mean of 137 seconds. The std dev
of all times was 5 seconds. So (129-137)/5
-1.6 In other words, the winning time was 1.6
standard deviations below the mean.
The winning long jump was 60cm longer than the
average 6m jump. The std dev of all jumps was
30cm. So 60/30 2 In other words, the
winning jump was 2 standard deviations above the
mean.
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MATH 1107 Using the STD DEV for Relative
Standing
Example from page 105 The SAT scores have a
mean of 1000 and a std dev of 200. The ACT
scores have a mean of 20.8 and a std dev of 4.8.
What ACT score would be equivalent to an SAT
score of 1220? First, lets convert the SAT score
of 1220 to a Z-score (1220-1000)/200
1.10 Next, lets solve for the ACT score that has
a Z-score of 1.10 (x-20.8)/4.8 1.10 X26.08
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MATH 1107 Using the STD DEV for Relative
Standing
Spot the Jack Russell weighs 19 pounds. The mean
weight for a Jack Russell Terrier is 16 pounds
with a std dev of 1.5 pounds. Desdi the Maine
Coon cat weighs 18 pounds and frequently kicks
Spots but around the house. The mean weight for
a Maine Coon is 17 pounds with a std dev of .75
pounds. Which animal is most in need of a diet?
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MATH 1107 Using the STD DEV for Relative
Standing
The 68-95-99.7 Rule (page 107) Many
distributions in life are normal or bell
shaped. When data follows a normal curve, the
following is true
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MATH 1107 Using the STD DEV for Relative
Standing
This is an important concept, because it allows
us to determine the probabilities associated with
certain outcomes. This is true, because the
Z-scores can be converted into probabilities of
occurrence.
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MATH 1107 Using the STD DEV for Relative
Standing

• Example from page 107
• Suppose it takes you 20 minutes to drive to
  campus, with a standard deviation of 2 minutes.
• How often will you arrive on campus in less
  than 22 minutes?
• How often will it take you more than 24
  minutes?
• 75 of the time you will arrive in X minutes or
  less. Solve for x.

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MATH 1107 Using the STD DEV for Relative
Standing
Fun EXCEL exercises!