 # Interpret Center and Spread of Data

Related Topics:
Common Core (Statistics & Probability)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn how to interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Common Core: HSS-ID.A.3

HS Math Interpreting Differences in Shape, Center, and Spread.
Example:
1. Jack normally makes really good grades in math class. All but one of his test scores are really high. His test scores are 97, 98, 94, 93, 99, and 70.
a) Is 70 an outlier?
b) I Jack's test score data skewed to the left or to the right?
c) WHich measure of spread is larger? Which measure of spread will give a more accurate picture of Jack's math performance?
d) Which measure of center is higher? Which measure of center gives a more accurate picture of Jack's math performance?
2. On the last math test 1st period's average score was an 85 with a standard deviation of 5 points. 2nd period's class average score was 88 with a standard deviation of 9 points. Which class was more consistent with their test scores? How do you know?
3. Why does the shape of the distribution of incomes for professional athletes tend to be skewed to the right?
4. Why does the shape of the distribution of test scores on a really easy test tend to be skewed to the left?
5. Why does the shape of distribution of heights of the students at your school tend to be symmetrical?
6. The height of Washington High School basketball players are: 5ft 9in, 5ft 4in, 5ft 7in, 5ft 6in, 5ft 5in, 5ft 3in, and 5 ft 7in. A student transfers to Washington High and joins the basketball team. Her height is 6ft 10in.
a) What is the mean height of the team before the new player transfers in? What is the median height?
b) What is the mean height after the new player transfers? What is the median height?
c) What effect does her height have on the team's height distribution and stats (Center and spread)?
d) How many players are taller than the new mean team height?
e) Which measure of center most accurately describes the team's average height? Explain.

Describing Histograms
A look at how to describe histograms based on center, spread, shape and outlier.
Some important keynotes:
When the data is skewed right, the mean will be larger than the median.
When the data is skewed left, the mean will be smaller than the median.
When the data is symmetrical, the mean and median will be about the same.
For bimodal data, you probably want to look at two separate sets of data rather than the one you're currently looking at.
Adjusting the class width may make it easier for you to see which measure of central tendency to use.
The only measure of spread we've talked about so far in class is range. This is found by taking the maximum and subtracting the minimum. It helps give us an idea of how spread out the data is. Maths Tutorial: Describing Statistical Distributions (Part 1 of 2)
How to describe histograms, boxplots, stemplots, and dotplots talking about shape, outliers, centre and spread? Maths Tutorial: Describing Statistical Distributions (Part 2 of 2)
How to describe outliers and spread on histograms, boxplots, stemplots, and dotplots? Center and Spread

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