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Statistics: Part III. SOL A.9. Objectives. Review vocabulary Variance Normal distributions Applications of statistics. Mean absolute deviation. Mean Absolute Deviation is a measure of the dispersion of data (how spread out the numbers are from the mean)

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objectives
Objectives
  • Review vocabulary
  • Variance
  • Normal distributions
  • Applications of statistics
mean absolute deviation
Mean absolute deviation
  • Mean Absolute Deviation is a measure of the dispersion of data (how spread out the numbers are from the mean)
  • Mean Absolute Deviation Formula:
  • Mean absolute deviation
standard deviation
Standard Deviation
  • Standard Deviation is a measure of the dispersion of data (how spread out numbers are from the mean)
  • The larger the standard deviation is, the more spread out the numbers tend to be from the mean.
  • Standard Deviation Formula:
mean absolute deviation and standard deviation
Mean absolute deviation and Standard Deviation
  • Mean Absolute Deviation (MAD) and Standard Deviation are statistics that are used to measure the dispersion (spread) of the data
  • Standard Deviation is a more traditional way to measure the spread of data.
  • Mean Absolute Deviation may be a better way to measure the dispersion of data when there are outliers since it is less affected by outliers.
z score
Z-Score
  • A z-score (or standard score) indicates how many standard deviations a data point is above or below the mean of a data set.
  • A positive z-score indicates that a data point is above the mean.
  • A negative z-score indicates that a data point is below the mean.
  • A z-score of zero indicates that a data point is equal to the mean.
z score1
Z-Score
  • The Z-Score Formula is:
variance
Variance
  • Variance is a measure of the dispersion of the data.
  • It is used to find the standard deviation and is equal to the standard deviation squared.
  • Variance formula:
what s normal
What’s Normal?
  • A normal curve is symmetric about the mean and has a bell shape.
what s normal1
What’s Normal?

Mean ( )

-1 Standard Deviation ( )

+1 Standard Deviation ( )

-2

+2

+3

-3

empirical rule
Empirical RUle
  • In a normal distribution with mean μ and standard deviation σ:
  • 68% of the data fall within σ of the mean μ.
  • 95% of the data fall within 2σ of the mean μ.
  • 99.7% of the data fall within 3σ of the mean μ.
application
Application
  • #1 Mr. Smith is planning to purchase new light bulbs for his art studio. He tested a sample of 10 Power-Up bulbs and found they lasted 4,356 hours on the average (mean) with a standard deviation of 211 hours. Then, he tested 10 Lights-A-Lot bulbs and found the following results.
  • 5,066 4,130 4,568 4,884 4,730
  • 5,122 4,910 4,866 4,779 4,721
application 1 continued
Application #1, continued
  • Which brand of light bulb has the greater average life span?
  • Mr. Smith bought 2 Lights-A-Lot bulbs. One bulb lasted for 5,150 hours and the other bulb lasted for 4,700 hours. Give the z-score for each bulb. Explain what each z-score represents.
  • Which brand of light bulb do you think that Mr. Smith should choose. Explain.
application1
Application
  • #2 The chart below lists the height (in inches) of 10 players from two NBA teams. Use the data to answer the following questions:
application question 2 continued
Application Question #2, Continued
  • Find the following for each team:
  • Chicago Bulls Toronto Raptors
  • =____________ = ____________
  • = ___________ = ____________
  • = ____________ = _____________

79.8

78.4

12.96

14.6

3.6

3.83

application question 2 continued1
Application Question #2, continued
  • B) Find the z-score for a height of 6’11” for each team:
  • Chicago Bulls: _____________
  • Toronto Raptors: ___________
  • C) Is it more likely that a player for the Bulls or the Raptors would be 6’11”? Explain.

1.201

0.889

He is more likely to play for the Raptors. Thez-score for that height for the Raptors is 0.889 and for the Bulls is 1.201. Therefore, a player who is 6’11” tall is more unusual (farther away from the mean) if he plays for the Bulls.

application question 2 continued2
Application Question #2, Continued
  • D) A player who is drafted by the Chicago Bulls has a z-score of -1.671. How tall is the player? Round to the nearest inch.
  • E) A player who is 6’7” tall has a z-score of -0.222. For which team does he play?
  • F) How many players on the Raptors are a height that isbetween -0.4 and 0.6 standard deviations from the mean?

6’0”

Toronto Raptors

5