Transcript Mean Median and Mode - Northside Middle School

PRE-ALGEBRA
Lesson 12-1 Warm-Up
PRE-ALGEBRA
Mean, Median, and Mode
(12-1)
What are
“measures of
central
tendency”?
measure of central tendency: a measure that tells us where the middle of a
bunch of data lies. The three most common measures of central tendency are
the mean, the median, and the mode.
What is a
“mean”?
mean (also called average): a number that describes the center (or middle) of a
set of data (numbers). It is the sum of the numbers divided by the numbers of
items added.
Example: The mean (average) of 7, 8, 7, 9, 10, 6, 9, 8, 2, 7 is:
7 + 8 + 7 +9 + 10 + 6 + 9 + 8 + 2 + 7 = 73 / 10 = 7.3
What is a
“median”?
median” – the “middle” number in a set of data (numbers) arranged from least
to greatest or greatest to least (If there are two numbers in the middle, find the
mean or average of the two numbers by adding them and dividing by 2)
Example: 2, 6, 7, 7, 7, 8, 8, 9, 9, 10, median = 7 + 8 / 2 = 15 / 2 = 7.5
What is a
“mode”?
mode: the number that comes up the “most”
Example: 2, 6, 7, 7, 7, 8, 8, 9, 9, 10
mode = 7
What is an
“outlier”?
outlier: the number that doesn’t belong with the rest (much higher or lower than
normal)
Example: 2, 17, 18, 19, 16, 17, 15, 18, 20, 17
outlier = 2
PRE-ALGEBRA
Mean, Median, and Mode
(12-1)
What is the
“range”?
range: the distance between the greatest and least value
Example: 2, 6, 7, 7, 7, 8, 8, 9, 9, 10
Range: 10 – 2 = 8
Example: Find the mean, median, mode, and outlier(s) for the Read-a-thon
graph.
mean: Add the numbers and divide by the number of items
added.
50 + 45 + 59 + 40 + 50 + 48 = 292 / 6 = 48.666…. 48.7
median: Put the numbers in order and find the one(s) in the
middle. Since there are two numbers in the middle, find the
mean (number in the middle) of those two numbers.
40, 45, 48, 50, 50, 59
48+50 = 98/2 = 49
mode: 50 appears most often = 50
range: highest – lowest number = 59 – 40 = 19
outlier: 59 appears to be an outlier, because it is 9 away from the closest value,
whereas the rest of the values are within 5 of each other
PRE-ALGEBRA
Mean Median and Mode
LESSON 12-1
Additional Examples
Rita’s quiz scores were 72, 96, 74, 80, 96, and 79. Find the
(a) mean, (b) median, (c) mode and (d) range of the data if you
leave out Latana’s pages.
a. Mean:
sum of data values
number of data values
=
72 + 96 + 74 + 80 + 96 + 79
6
497
6

83.8
=
Rita’s mean or average test score is about 84.
PRE-ALGEBRA
Mean Median and Mode
LESSON 12-1
Additional Examples
(continued)
b. Median: 72, 74, 79, 80, 96, 96
Write the data in order.
The median is the average of the middle numbers = 79 + 80 / 2 = 79.5 .
c. Mode: Find the data value that occurs most often.
The mode is 96.
d. Range: Greatest value – Least value = 96 – 72 = 24.
PRE-ALGEBRA
Mean Median and Mode
LESSON 12-1
Additional Examples
How many modes, if any, does each have? Name
them.
a. $1.10 $1.25 $2.00 $2.10 $2.20 $3.50
No values are the same, so there is no mode.
b. 1 3 4 6 7 7 8 9 10 12 12 13
Both 7 and 12 appear more than the other data values.
Since they appear the same number of times, there are two modes.
c. tomato, tomato, grape, orange, cherry, cherry, melon, cherry, grape
Cherry appears most often. There is one mode.
PRE-ALGEBRA
Mean Median and Mode
LESSON 12-1
Additional Examples
Use the data: 7%, 4%, 10%, 33%, 11%, 12%.
a. Which data value is an outlier?
The data value 33% is an outlier. It is an outlier because it is 21%
away from the closest data value.
b. How does the outlier affect the mean?
77
6
12.8
Find the mean with the outlier.
44
5
8.8
Find the mean without the outlier.
12.8 – 8.8 = 4
The outlier raises the mean by about 4 points or 4 / 12.8  31%
PRE-ALGEBRA
Mean, Median, and Mode
(12-1)
How do you
choose the
best measure
of central
tendency to
describe a set
of data?
Example Situation: The favorite movie of students in the eight grade.
Best Measure  Mode: The mode is the most appropriate measure, since you’re
trying to find the one that most people like (“favorite”) and mode describes the most
frequent item chosen.
Example Situation: The daily high temperature during a week in July..
Best Measure  Mean: The mean describes what the high temperatures are most
likely around (There probably won’t be an outlier, so the mean should be pretty
accurate.)
Exampe Situation: The distance students travel to school.
Best Measure  Median: The median is more appropriate, since there is very
likely at least one outlier for this set of data (at least one student probably lives
much farther from school than the majority), which would influence the mean but
not the median (middle value or values)
PRE-ALGEBRA
Mean Median and Mode
LESSON 12-1
Additional Examples
Which measure of central tendency best describes
each situation? Explain.
a. the monthly amount of rain for a year
Mean; since the average monthly amount of rain for a year is not
likely to have an outlier, mean is the appropriate measure. When
the data have no outliers, use the mean.
b. most popular color of shirt
Mode; since the data are not numerical, the mode is the appropriate
measure. When determining the most frequently chosen item, or when
the data are not numerical, use the mode.
PRE-ALGEBRA
Mean Median and Mode
LESSON 12-1
Additional Examples
(continued)
c. times school buses arrive at school
Median; since one bus may have to travel much farther than other
buses, the median is the appropriate measure. When an outlier may
significantly influence the mean, use the median.
PRE-ALGEBRA
Mean Median and Mode
LESSON 12-1
Lesson Quiz
Which measure of central tendency best describes each situation?
1. numbers of legs on the animals in a zoo
mode
2. favorite digits (from 0 to 9) of the students in a class
mode
3. numbers of days-per-student that students are absent from school
median
4. test scores
mean
PRE-ALGEBRA