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 , 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.

x

Ex. 1 Find the mean, median, and mode of the test scores below.

42+72+...+75:x =

18Mean =76

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

77 +81:

2Median =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 value2. 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.

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)

Steps to finding the standard deviation

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)!

Quiz Scores:

19, 15, 21, 17, 25, 18, 17

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

Variance = 84.2 Standard Deviation = 9.2

2nd period 3rd period

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?

Mean = 80 Mean = 80

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.

X =5

Variance = 6.8

Standard Deviation = 2.6

SET A 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)