Warm-UpLook at our planes dotplotWhat percent of people do you think flew

their plane more than 30 feet?What percent of people do you think flew

their plane less than 5 feet?

Describing Location in a Distribution

Section 2.1

Measuring PositionPercentile – the pth percentile of a

distribution is the value with p percent of the observations less than it.

Example – Alexis is in the 95th percentile for height for her age…that means that 95% of three year olds are shorter than her.

What are some other examples where you have already seen percentiles in your daily life?

ExampleUse the scores of Mr. Pryor’s first statistics

test to find the percentiles for the following students:Norman – earned a 72

Katie – earned a 93

The two students who earned 80’s

Scores of class: 79 81 80 77 73 83 74 93 78 80 75 67 73 77 83 86 90 79 85 83 89 84 82 77 72

Cumulative Relative Frequency GraphsThese are made with percentiles!Example (President’s age at Inauguration):

Age 40-44

45-49 50-54 55-59 60-64 65-69

Frequency

2 7 13 12 7 3

Take that data and graph it!

Questions based on that…What percent of presidents were between

55 and 59?

Was Barack Obama, who was inaugurated at age 47, unusually young?

Estimate and interpret the 65th percentile of the distribution.

Z-ScoresStandardized Value (Z-Score) – if x is an

observation from a distribution that has known mean and standard deviation, the standardized value of is

“how many standard deviations is something above or below the mean”

Use Mr. Pryor’s tests…Mean is 80Standard deviation is 6.07Find the z-score for Katie – scored a 93

Find the z-score for Norman – earned a 72

Our planes answers!In order to find the actual percentiles

(tomorrow) we need to find the z-scores of each observation I asked you about.

30 feet

5 feet

Computer Outputs

Transforming DataEffect of Adding (or Subtracting) a constant: adding

the same number to each observation Adds that number to measures of center and location

(mean, median, quartiles, percentiles)Does not change the shape of the distribution of

measures of spread (range, IQR, standard deviation)

Effect of Multiplying (or Dividing) by a constant:Multiplies (divides) measures of center and location

(mean, median, quartiles, percentiles) by bMultiplies (divides) measures of spread (range, IQR,

standard deviation) by (can’t have a negative variability)

Does not change the shape of the distribution

ExamplesLook at our planes – What if I added three feet to every

observation?

What if we multiplied every observation by 2?

HomeworkPg 105 (1-18)