Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
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.
continue notes on back
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.