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Measures of Central
Tendency and
MM2D1 Using sample data, students will make informal inferences about population
means and standard deviations...
a. Understand and calculate the means and standard deviations of sets of data.
b. Use means and standard deviations of random samples with the corresponding population
parameters, including those population parameters for normal distributions. Observe that the
different sample means vary from one sample to the next. Observe that the distribution of the
sample means has less variability than the population distribution.
Central Tendency
Measure of Central Tendency- a number used to
represent the center or middle of a set of data
Shown as x with a line---- and read “x-bar.”
MODE-most often, may be one, none, or more
than one
MEDIAN-(think of a road) middle when written in
numerical order. Could be the average of the
middle two if there is an even number of terms.
Mean, Median, Mode
The test scores received by students on a
history exam are listed below. Which
measure of central tendency best
represents the data?
65, 68, 71, 77, 82, 86, 88, 93, 95, 97
Mean, Median, Mode
65, 68, 71, 77, 82, 86, 88, 93, 95, 97
Mean and median represent best. Mode is
greater than the rest of the data.
Measures of Dispersion
Disperse-to spread out
Range-greatest minus the least
Standard Deviation (σ-read “sigma”)
Measures of Dispersion
In a golf tournament, the top 6 men’s scores are
given. Compare the mean and standard
deviation of the set of scores.
Men’s: 65, 68, 70, 72, 73, 75
Measures of Dispersion
Men’s mean 70.5
Men’s standard deviation
Square root(65-70.5)2+(68-70.5)2+…….
Square root
Square root of 65.5
6 =3.3
Try your samples
Personal project
Choose one of the following numbers to collect:
Your grades from the last 6 grades.
The weights of 6 of your peers.
The number of siblings of each member of the class.
The number of hours you study each night –Monday-Friday
Find the mean, median, mode, range, and standard
deviation of your choice.
Report it to the class by presentation.