WARM UPYEAR 190

01920

1940

1960

1980

2000

PERCENTAGE

13.6 13.2 8.8 5.4 6.2 10.4

A: Make a bar graph of this data

B: Why is it inappropriate to make a circle graph of this data?

PROPERTIES OF THE MEAN

The Mean of 2, 3, and “N” numbers

FINDING THE MEAN (2 NUMBERS) To find the mean of two numbers, you

add them and divide them by 2. So if the numbers are “a” and “b” and

the mean is “m” then:

EXAMPLEIn January in Dulut, Minnesota, a typical

high temperature is 18 degrees Fahrenheit and a typical low temperature is -1 degrees Fahrenheit. The mean of these numbers is:

Notice that 2 • 8.5 = 17 (the sum of the two temperatures)

FINDING THE MEAN (3 NUMBERS) To find the mean of 3 numbers, you add

them and divide the sum by 3. If the numbers are “a” “b” and “c” then:

PRACTICE PROBLEM Mykia has scored 86, 83, 91, and 75 on

her first four tests in a class. What score does she need on the fifth

test to average 85 for all five tests?

GEOMETRICALLY PROVING THE MEAN Here are the scores of 10 students on a

quiz:100, 100, 100, 100, 90, 60, 60, 60, 50, 50

The sum of the scores is 770, so the mean is 77.

BALANCE PROPERTY If “m” is the mean of a set of numbers. Then the sum of the distances to “m”

from the numbers greater than “m” in the set equals the sum of the distances to “m” from the numbers less than “m” in the set.

How you may ask??

BALANCE PROPERTY

PRACTICE MAKES PERFECT Ishi has a mean score 57 on the first 5

of 6 tests she must take this semester. She wants to know what she has to score on the last test to average 60 for all 6 tests

A: Answer Ishi’s question by solving an equation

B: Answer Ishi’s question by calculating distances from the mean.