Warm-Up
 Look at our planes dotplot
 What 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?
Section 2.1
Describing Location in a Distribution
Measuring Position
 Percentile – 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?
Example
 Use 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 Graphs
 These 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-Scores
 Standardized Value (Z-Score) – if x is an observation from a
distribution that has known mean and standard deviation, the
standardized value of is
𝑥 − 𝑚𝑒𝑎𝑛
𝑧=
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑜𝑛
“how many standard deviations is something above or below the mean”
Use Mr. Pryor’s tests…
 Mean is 80
 Standard deviation is 6.07
 Find 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 Data
 Effect 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 b
 Multiplies (divides) measures of spread (range, IQR, standard
deviation) by 𝑏 (can’t have a negative variability)
 Does not change the shape of the distribution
Examples
 Look at our planes –
 What if I added three feet to every observation?
 What if we multiplied every observation by 2?
Homework
 Pg 105 (1-18)