Geometry & Finite H
Mr. Russo
Name: _______________________
Date: _______________________
Histograms, Measures of Position & Z-scores
The histogram below shows the distribution of the age of presidents at the time of their inauguration. Use the
histogram to complete the frequency table.
Age Range
Number of Presidents
40 - 44
45 - 49
50 - 54
55 - 59
60 - 64
65 - 69
Note: the 1st bar looks like it goes from 40-45, but it really only goes from 40-44. 45 is included in the 2nd bar.
Approximately how many days was the 2 PM temperature 70 degrees or more?
Shape:
The 6 images below show you some typical shapes of distributions. Describe the 2 histograms from the
previous page.
Presidents:
2 PM Temperature:
If Carly scored 610 on her Math SAT and 600 on her Verbal SAT, she scored higher on math, obviously. BUT,
which section did she do better on, relative to everyone else that took the test?
Questions like this require us to use the statistical technique of STANDARDIZING.
Example #1: If the mean SAT score for math is 520 with a standard deviation of 100, and the mean SAT score
for verbal is 500 with a standard deviation of 95, find Carly’s z-score for each test. Which test did she do better
on relative to other test-takers?
Example #2: Record your height in inches: ____________________ inches.
Record the mean and standard deviations of heights for your gender from the table given in class:
Mean = __________________
Standard Deviation = _________________
Use the formula, your height converted to inches, and the mean and standard deviation of heights for
your gender to find your z-score.
Z=
Fill in the blanks:
If your z-score is positive, your height is ________________ the mean for your gender.
If your z-score is negative, your height is ________________ the mean for your gender.
If your z-score is zero, your height is ____________________the mean for your gender.
Example #3: Jenny earned a score of 76 on her statistics test. The class mean was 80 and the standard deviation
was 6.07. She earned a score of 82 on her chemistry test. The class mean was 85 and standard deviation of 4.
On which test did Jenny perform better relative to the rest of her class?
Understanding Percentiles:
A percentile is a measure used in statistics indicating a value below which a certain percentage of a group falls.
For example: If you were to score in the 90th percentile on the SAT math section, that would mean that you
scored _______________ than 90% of other people taking the same test. (IT DOES NOT MEAN THAT
YOU SCORED A 90%!!!)
Example #4: 2000 people took the midterm exam in a college calculus course. Mark scored a 88 which placed
him in the 76th percentile of all test takers.

What percentage of people did Mark score better than?

About how many people scored lower than Mark? Higher than Mark?
Summary:
 Histograms are a way to display continuous data, and can help us see the shape of the data (skewed,
symmetrical, etc.)
 Z-scores can help us determine how far a data point is from the mean.
 Percentiles tell us a percent of how many data points fall below a specific value, they don’t actually give
you the percent you scored.
HW 3
1.)
a.
The median cost is in which interval on the graph?
b.
How many colleges cost between $3,000 and $3,500?
c.
Is a college that costs $3,000 included in the above count? Is $3,500?
d.
From the data, what percent of colleges cost $6,000 or more?
2.) Noah and Rita are working on a report for economics. They surveyed 95 farmers and recorded the number
of acres of corn they had planted. The histogram displays the data they collected.
a. Describe the shape of the distribution.
b. How many farmers planted fewer than 2 acres of corn?
c. What % of farmers planted fewer than 2 acres of corn?
d. Estimate the median number of acres of corn planted.
e. Do you think the mean number of acres of corn planted is higher, lower, or about the same as the
median? Explain.
3.) At a large university, 1500 students took a final exam in chemistry. Frank Stein learned that his score of 76
placed him in the 88th percentile of test takers.
a. Roughly how many students scored lower than Frank?
b. Roughly how many students scored the same or higher than Frank?
c. Mary was placed at the 95th percentile. Describe how she performed on the test relative to Frank.
4.) Calculate the appropriate z-scores to answer the following question:
(I.e., relative to everyone else that took it.)
5.