slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Interpreting Center & Variability PowerPoint Presentation
Download Presentation
Interpreting Center & Variability

Loading in 2 Seconds...

play fullscreen
1 / 11

Interpreting Center & Variability - PowerPoint PPT Presentation


  • 80 Views
  • Uploaded on

Interpreting Center & Variability. Density Curves. Can be created by smoothing histograms ALWAYS on or above the horizontal axis Has an area of exactly one underneath it Describes the proportion of observations that fall within a range of values

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Interpreting Center & Variability' - haviva-craft


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Interpreting

Center &

Variability

density curves
Density Curves
  • Can be created by smoothing histograms
  • ALWAYS on or above the horizontal axis
  • Has an area of exactly one underneath it
  • Describes the proportion of observations that fall within a range of values
  • Is often a description of the overall distribution
  • Uses μ & σ to represent the mean & standard deviation
z score
z score

Standardized score

Creates the standard normal density curve

Has μ = 0 & σ = 1

what do these z scores mean
What do these z scores mean?

-2.3

1.8

6.1

-4.3

2.3 σ below the mean

1.8 σ above the mean

6.1 σ above the mean

4.3 σ below the mean

slide5

Jonathan wants to work at Utopia Landfill. He must take a test to see if he is qualified for the job. The test has a normal distribution with μ = 45 and σ = 3.6. In order to qualify for the job, a person can not score lower than 2.5 standard deviations below the mean. Jonathan scores 35 on this test. Does he get the job?

No, he scored 2.78 SD below the mean

chebyshev s rule
Chebyshev’s Rule

The percentage of observations that are within k standard deviations of the mean is at least

where k > 1

can be used with any distribution

At least what percent of observations is within 2 standard deviations of the mean for any shape distribution?

75%

chebyshev s rule what to know
Chebyshev’s Rule- what to know
  • Can be used with any shape distribution
  • Gives an “At least . . .” estimate
  • For 2 standard deviations – at least 75%
normal curve
Normal Curve

Bell-shaped, symmetrical curve

Transition points between cupping upward & downward occur at μ + σ and μ – σ

As the standard deviation increases, the curve flattens & spreads

As the standard deviation decreases, the curve gets taller & thinner

empirical rule
Empirical Rule

Approximately 68% of the observations are within 1σof μ

Approximately 95% of the observations are within 2σof μ

Approximately 99.7% of the observations are within 3σof μ

Can ONLY be used with normal curves!

slide10

The height of male students at WHS is approximately normally distributed with a mean of 71 inches and standard deviation of 2.5 inches.

a) What percent of the male students are shorter than 66 inches?

b) Taller than 73.5 inches?

c) Between 66 & 73.5 inches?

About 2.5%

About 16%

About 81.5%

slide11

Remember the bicycle problem? Assume that the phases are independent and are normal distributions. What percent of the total setup times will be more than 44.96 minutes?

First, find the mean & standard deviation for the total setup time.

2.5%