Download Making it Relevant: Comparing Data Sets by

Warm Up
1. Tell me the mean and the median for the
following data sets
Math Test Scores
Class 1: 99, 76, 84, 70, 45, 73, 88
Class 2: 75, 100, 65, 70, 88, 95, 94
2. Which class did better? Elaborate and clarify
with details to support your answer.
Comparing Data Sets by
Measures of Center
(Central Tendency)
and
Spread
Measures of Center
(Central Tendency)
• Tells us something about the middle of the
distribution.
• Mean – tells us the average value
• Median – tell us the middle value
• Mode – tell us the most frequent value
-Median and Mean can be effected by extreme
values (very high or very low scores) outliers
Measures of Center:
Normal Distribution
-in a normal distribution, the mean, median and
mode is the max. value (highest point) of the
graph:
Shapes of Distribution
Non Symmetric
Skewed Left (negatively skewed)
Left Skew
tail
Skewed Right (positively skewed)
Right Skew
tail
5
Right Skew
Skew on shape of distribution in relation to mean and
median
If you have right skew, the mean will be to the right of
(greater than) the median, as the mean follows the tail of
the distribution.
median
mean
Right Skew
tail
6
Left Skew
Skew on a dot plot in relation to mean and median
If you have left skew, the mean will be to the left of
(less than) the median, as the mean follows the tail
of the distribution.
median
mean
tail
Left Skew
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Measure of Center: Box Plots
• The median value on a box plot is the line drawn
inside the box.
• Tell me the median for each of the different
countries:
Center: Comparing Data Sets
• Compute and compare the mean for the three data
sets graphed below:
• A: Class 1; B: Class 2; C: Class 3
Math Test Scores
Explain your reasoning.
Measures of Spread
• Interquartile Range =
Upper quartile (Q3) – lower quartile (Q1)
Example: What is the interquartile range (IQR) for
the following first and second shifts ? Compare
the two.
Measures of Spread
• Standard Deviation – shows the
distance/spread of the data points from the
mean.
• High value – means the spread of values from
the mean is far.
• Low Value – means the spread of values from
the mean is close
Standard Deviation
Turn and Talk: Standard Deviation
• Compare, and elaborate on, the spread of the
two data distributions shown in the graph
below:
Title: Number of Video Games Owned
Key
Blue = high school
students
Red = College
students
Classwork
For each of the two scenarios below, compare and interpret the center and
spread of the data sets.
Graph 1
Title: Life expectancy
for different animals
Key
Red = Turtle
Blue = Wolf
Green = Ant
Graph 2