This document provides a tutorial on measures of central tendency including mean, median, mode, and range. It defines each measure and provides examples of how to calculate them using a sample data set of numbers. It also discusses how these measures are used in policy debates and to determine eligibility for federal grants and foundation funding, as well as to measure the impact of community programs.

1. A S H O RT P U B L I C S E RV I C E T U T O R I A L
MEAN, MEDIAN, MODE &
RANGE

2. MEASURES OF CENTRAL TENDENCY
• All four are called measures of central tendency.
• They are ‘short hand’ ways to describe a series of
numbers
• Family income
• Grades
• Height
• Each one has strengths and weaknesses BUT none is a
complete description of the series.

3. MEAN
• The mean, sometimes called the arithmetic mean, is the average of
series of values.
• Consider the following values:
• 13, 18, 13, 14, 13, 16, 14, 21, 13
• To calculate the mean, add and then divide by the number of values:
• (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
• Note that the mean, in this case, isn't a value from the original list. This
is a common result. You should not assume that your mean will be one
of your original numbers.

4. MEDIAN
• The median is the middle value when the numbers are in numerical order
from low to high:
• 13, 13, 13, 13, 14, 14, 16, 18, 21
• There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 =
10 ÷ 2 = 5th number:
• 13, 13, 13, 13, 14, 14, 16, 18, 21
• The median is 14.
• The formula for the place to find the median is "([the number of data points] +
1) ÷ 2", but you don't have to use this formula. You can just count in from both
ends of the list until you meet in the middle, if you prefer, especially if your list
is short. Either way will work.

5. MEDIAN
• If the series contains an even number of values, the median is the average of
the two middle values
• 13, 13, 13, 13, 14, 14, 16, 18, 21 21
• There are ten numbers in the list, so the ‘middle one’ will be average of the
two values in the middle.
• In this example, the median is still 14.

6. MODE
• The mode is the number that is repeated more often
than any other
• 13, 13, 13, 13, 14, 14, 16, 18, 21
• 13 is the mode.
• The "mode" is the value that occurs most often. If no
number in the list is repeated, then there is no mode for
the list.

7. RANGE
• The difference between the largest and smallest in a set
of numbers.
• 13, 18, 13, 14, 13, 16, 14, 21, 13
• The largest value in the list is 21, and the smallest is 13,
• Range is 21 – 13 = 8.

8. DESCRIPTION BY CENTRAL TENDENCY
• Described in terms of central tendency our series 13, 18,
13, 14, 13, 16, 14, 21, 13
• mean: 15
• median: 14
• mode: 13
• range: 8

9. I A LWAY S H AT E D M AT H
WHY SHOULD I CARE?

10. POLICY DEBATES
• US mean (average) household income was $65,751 in
2014.
• Median household income in 2014 was $53,719.
• The mean is higher because a rather small group of high
income households raise the average.
• Choice of the mean or median impacts income inequality
perceptions.

11. FEDERAL & FOUNDATION GRANT
ELIGIBILITY REQUIREMENTS
• Housing and Urban Development
• HUD Section 8 Income Limits begin with the production of Median
Family Income (MFI) estimates.
• Tony Hawk Foundation
• If the Median Household Income in the city or town where the skatepark
will be located in is significantly higher than your State’s Median
Household Income, your organization is not eligible to apply for a grant.
• Opus Bank Community Foundation
• proposals targeted to Low or Moderate Income(LMI) persons or
communities. LMI is defined as less than 80% of an area's median
income.

12. FEDERAL & FOUNDATION GRANT
PERFORMANCE MEASURES
• The Rapides Foundation (Central Louisiana)
• Uses change in median household income to gauge grantee’s program
impact over time
• Community Development Block Grant
• “We are pleased with the City’s housing assistance performance, in
particular its Residential Rehabilitation program that resulted in repairs
to thirteen (13) homes to benefit low-income households.”
• Letter from CDBG to City of Miramar FL

13. OTHER PUBLIC POLICY RELATED
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