Download Measure of Central Tendency and Spread of Data

Measure of Central Tendency
and Spread of Data
Notes
are numerical values
used to summarize and
compare sets of data.
Measure of Central Tendency:
Mean (average) – the means is denoted by
x , which is read as “x-bar”.
Median – is the middle number when the numbers are written in order.
Mode – is the number or numbers that occur most frequently.
Ex. 1 Find the mean, median, and mode of the test scores below.
42 + 72 + ... + 75
=76
Mean : x =
18
Median – 1st order the test scores:
42, 45,52,57,58,72, 75, 75, 77, 81, 82, 83, 89, 93, 95, 97, 97, 98
Since there is an even number of
scores, the median is the average of
the two middle scores
Median :
77 + 81
2
=79
Mode – There are two modes, 75 and 97, because these
numbers occur most frequently.
A Measure of Dispersion
A measure of dispersion is a statistic that
tells you how spread out your data
values are:
2 ways to measure dispersion:
1. Range: Greatest value – Least value
2. Standard Deviation
A SMALL deviation indicates
that the data values are pretty
close to the mean.
A LARGE deviation indicates
that the data values are spread
apart from the mean.
Standard Deviation (σ) - is a measure of
dispersion that tells you how spread out your
data is relative to your mean (the middle of your
data)
Quiz Scores:
Steps to finding the standard deviation
19, 15, 21, 17, 25, 18, 17
1. Work out the mean!
2. Take each number in your list and
subtract it from the mean and square it
3. Take the average of all the squared
differences (from step 2). This is
called the VARIANCE (σ2)
4. Then square root the variance and this
is your STANDARD DEVIATION (σ)!
I have provided you with
a table to help organize
these steps!!!
Your Turn, again:
1. Find the range and standard deviation of the data of set.
2. Compare the means and standard deviations for the two sets
of test scores:
2nd period: 65,70,75,75,80,83,87,90,95
3rd period: 32,59,68,71,94,96,98,100,102
2nd period
Mean = 80
Variance = 84.2
Standard Deviation = 9.2
3rd period
Mean = 80
Variance = 514.4
Standard Deviation = 22.7
Explain the difference in the two sets of tests. How are they
alike, and how are they different?
Your Turn:
1. Find the range and standard deviation of the data of set.
2. Compare the means and standard deviations of Set A and Set B.
SET A
X =5
Variance = 6.8
Standard Deviation = 2.6
SET B
X =6
Variance = 2
Standard Deviation = 1.4
Set B has a larger mean than Set A. The standard deviations tell
us that the data values in Set B vary less than Set A.
Class work!
Day 1:
Workbook Page 272
#1-10 (do not do the standard deviation)
Day 2:
Workbook page 272
#5-8 (standard deviation)
Homework!
Day 1:
Page 261
#1-12 (do not do the standard deviation)
Day 2:
Page 261
#8-12 even (standard deviation)