Cornell NotesWorkplace Math 10

CHAPTER: CENTRAL TENDENCIES TOPIC: MEAN, MEDIAN, MODE, AND RANGE

DATE:________________________HOMEWORK:

KEY TERMS: DEFINITION:

mean the average; the sum of the data divided by the total number of items

in the data set

Mean=∑ of all data valuesnumber of dataitems

median the middle number in the data set when the data has been ordered from

the least to the greatest

mode the number that occurs the most often in a set of data

range measures the variance or the distance between the highest data piece

and the lowest data piece; subtract the largest number and the smallest

number to calculate the range

QUESTIONS/EXAMPLES:

NOTES:

Example 1

Quiz Scores

47 40 43 45

49 41 49 44

43 41 44 49

44 50 41 44

mean=47+40+43+45+49+41+49+44+43+41+44+49+44+50+41+4416

¿71416

=44.625

The table shows the quiz scores for 16 students. Find the mean.

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QUESTIONS: NOTES:Example 2 Find the median form the following data set:

20yd, 17 yd, 11yd, 20 yd, 15 yd, 7 yd

Put the data set into 7 yd, 11 yd, 15 yd, 17 yd, 20 yd, 20 yd

numerical order from 3 from the left = 15; 3 from the right = 17; exact middle = 16

least to greatest median=15+172

=16

Example 3 Find the mode of the following data set:

Data set: 50 mi, 45 mi, 45 mi, 52 mi, 49 mi, 56 mi, 56 mi

45 mi and 56 mi both occur twice in the data set

It is possible to have Modes = 46 mi and 56 mi

more than one mode

Example 4 Find the range of the following data set:

Data set: 47, 40, 43, 45, 49, 41, 49, 44

Highest number: 49 Lowest number: 40

Range = highest number – lowest number

= 49 – 40 = 9

Example 5 Find the mean, median, mode, and range of the following:

Data set: 5, 9, 6, 6, 11, 8, 4

mean=5+9+6+6+11+8+47

=497

=7

median=4,5,6,6,8,9,11=6

mode=6 asis∈the data set twice

range=11−4=7

Example 6 Find the mean, median, mode, and range of the following data set:

Data set: 3, 7, 2, 5, 5, 6, 5, 10, 11, 5

mean=3+7+2+5+5+6+5+10+11+510

=5910

=5.9

median=2,3,5,5,5,5,6,7,10,11=5

mode=5 asis∈the data set 4׿

range=11−2=9

Choose the Best Measure of Central Tendency

Measure Most Useful When …

Mean Data has no outliers (numbers that are not near the rest)

Median Data set has no outliers

There are no big gaps in the middle of the data

Mode Data set has many identical numbers

Range Describing the spread of the data

Example 7 Amir and Melanie’s weekly test scores were: 4,5,8,9,9

Which measure(s) of central tendency best describe the data?

mean=4+5+8+9+95

=355

=7 median=8

mode=9 range=9−4=5

The mean and the median are the best measures of the data. Mode does

work as it represents the highest score; range gives us the spread of the

scores so is not useful.

Example 8 Students have taken a vote on the new official school colours for sports

Uniforms. The number of votes for each colour is as follows:

Red Orange Yellow Green Blue Purple

7 4 1 5 6 10

As this was a vote for the new colour, only the mode is of any real

importance as the most popular colour wins. So mean and median

are not necessary – only mode.

Example 9 Compare Median and Mode

Suki paid the following amounts for her last six pairs of jeans before tax:

$44, $38, $45, $49, $125, $50

a) What are the median and mean jean prices?

mean=38+44+45+49+50+1256

=$ 58.50

median=$ 47

QUESTIONS: NOTES:b) Which measure of central tendency best describes these data?

The value of $125 is very different from the rest – known as an

outlier. This alters the mean significantly, but does not affect

the median as much. So, median is a better measure.

Example 10 Choose best measure of central tendency to describe the data below:

mean=4+4+4+…16+1617

=14117

=8.3mi

median=4,4,4,4,4,5,5,5,6,6,14,15,15,15,15,16,16=6 mi

mode=4 mi∧15 mi

range=16−4=12mi

Mean is not the best fit because everyone ran more or few then 8 miles.

Median is not the best fit because of the large gap in the middle of

the data set.

Mode is the best fit because it shows the low and high averages of the

Runners.

Range is not a good fit because more runners ran less than 12 miles.