Introductory Statistics

Lesson 2.3 A

Objective: SSBAT find the mean, median, and mode of data.

Standards: M11.E.2.1.1

Measure of Central Tendency

A value (number) that represents a typical or central entry of a data set

3 commonly used measures are MEAN, MEDIAN, and MODE

Example: The ages of employees in a department are listed. What is the mean age?

34, 27, 50, 45, 41, 37, 24, 57, 40, 38, 62, 44, 39, 40

The mean age of the employees is 41.3 years.

Mean

Add all of the numbers together and Divide by the number of values in the set

Population Mean

represents the population mean

N represents the number of entries in a Population

Sample Mean

represents the sample mean

n represents the number of entries in a Sample

Example: The prices (in dollars) for a sample of roundtrip flights from Chicago, Illinois to Cancun, Mexico are listed. What is the mean price of the flights?

872, 432, 397, 427, 388, 782, 397

= 872 + 432 + 397 + 427 + 388 + 782 + 397

= 3695

=

527.90

The mean price of the flights is about $527.90.

Median

The number that is in the middle of the data when it is ordered from least to greatest

1. Write the numbers in order from least to greatest2. Find the middle number

If there are 2 middle numbers, Add them and divide by 2

Example: Find the Median of the flight prices from 1.

872, 432, 397, 427, 388, 782, 397

388, 397, 397, 427, 432, 782, 872

The Median flight price is $427.

Example: The ages of a sample of fans at a rock concert are listed. Find the median age.

26, 27, 19, 21, 23, 30, 36, 21, 27, 19,

Mode

The number that occurs the most in the data set

If no entry is repeated, there is No Mode

There may be more than 1 mode

Bimodal A data set that has 2 modes

Example: Find the mode of the flight prices from #1.

872, 432, 397, 427, 388, 782, 397

The mode price is $397.

Example: Find the mode of the employee ages.

24, 27, 27, 34, 37, 38, 39, 40, 40, 44, 49, 57

The mode age is 27 and 40

Example: A sample of people were asked which political party they belonged to. The results are in the table below.

What is the Mode of their response?

Political Party Frequency, fDemocrat 34

Republican 56

Other 21

Did not respond 9

The response with the greatest frequency is Republican therefore the MODE is Republican

Example: Find the Mean, Median, and Mode

Football Team Points

Stem Leaf

0 6

1 2 3 3 7

2 0 3 4 4 7 8

3 0 7 8

Key: 1│2 = 12 points

Mean: 22.3

Median: 23.5

Mode: 13 and 24

Example: Find the Mean, Median, and Mode

Entries: 1, 3, 3, 6, 6, 7, 8, 8, 8, 8, 10

Mean: 6.2

Median: 7

Mode: 8

Find the Mean, Median and Mode of the data set.

20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 25, 25, 78

Mean, : 25.3

Median: 21.5

Mode: 20

Which measure of central tendency best describes this data set?

Median

Outlier

A data entry that is a lot bigger or smaller than the other entries in the set

Outliers cause Gaps in the data

Conclusions made from data with outliers can be flawed

MEAN

- There is only one mean for each data set- It is the most commonly- It takes into consideration all data entries- It is affected by Extreme Values – Outliers

MEDIAN

- There is only one median for each data set- Extreme values (outliers) do NOT affect the median

MODE

- Use when you are looking for the most popular item- Use when you have non-numerical data- When no value repeats there is no mode

Homework

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