weighted mean - new diet cola
TRANSCRIPT
3.1 - 1
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored Number Surveyed1 40% 10002 30% 30003 50% 800
3.1 - 2
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Identify which column is the variable (x) and which column is the weights (w).
Area % Favored Number Surveyed1 40% 10002 30% 30003 50% 800
3.1 - 3
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Identify which column is the variable (x) and which column is the weights (w).- The values you are finding the weighted mean of is the variable
% Favored is the variable (x)
Area % Favored (x) Number Surveyed 1 40% 10002 30% 30003 50% 800
3.1 - 4
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Identify which column is the variable (x) and which column is the weights (w).- The values you are finding the weighted mean of is the variable
% Favored is the variable (x)- Use the Numbered Surveyed (w) as the weights. Area 2 will be weighted more because more people were surveyed.
Area % Favored (x) Number Surveyed (w)1 40% 10002 30% 30003 50% 800
3.1 - 5
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w)1 40% 10002 30% 30003 50% 800
wxwX )(
3.1 - 6
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w)1 40% 10002 30% 30003 50% 800
wxwX )( Create a column for w∙x
3.1 - 7
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 10002 30% 30003 50% 800
wxwX )( Create a column for w∙x
3.1 - 8
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1000 40*1000 = 40,0002 30% 30003 50% 800
wxwX )( Create a column for w∙x
3.1 - 9
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1000 40*1000 = 40,0002 30% 3000 30*3000 = 30,0003 50% 800
wxwX )( Create a column for w∙x
3.1 - 10
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1000 40×1000 = 40,0002 30% 3000 30×3000 = 30,0003 50% 800 50×800 = 40,000
wxwX )( Create a column for w∙x
3.1 - 11
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1000 40×1000 = 40,0002 30% 3000 30×3000 = 30,0003 50% 800 50×800 = 40,000
wxwX )( Sum the column of w∙x
3.1 - 12
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1000 40×1000 = 40,0002 30% 3000 30×3000 = 30,0003 50% 800 50×800 = 40,000
wxwX )( Sum the column of w∙x
Σ(w∙x) = 110,000
3.1 - 13
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1000 40×1000 = 40,0002 30% 3000 30×3000 = 30,0003 50% 800 50×800 = 40,000
wxwX )(
Sum the column of w
Σ(w∙x) = 110,000
3.1 - 14
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1,000 40×1000 = 40,0002 30% 3,000 30×3000 = 30,0003 50% 800 50×800 = 40,000
wxwX )(
Sum the column of w
Σ(w∙x) = 110,000Σw = 4,800
3.1 - 15
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1,000 40×1000 = 40,0002 30% 3,000 30×3000 = 30,0003 50% 800 50×800 = 40,000
wxwX )(
Σ(w∙x) = 110,000Σw = 4,800
3.1 - 16
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1,000 40×1000 = 40,0002 30% 3,000 30×3000 = 30,0003 50% 800 50×800 = 40,000
800,4000,110)( w
xwX
Σ(w∙x) = 110,000Σw = 4,800
3.1 - 17
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1,000 40×1000 = 40,0002 30% 3,000 30×3000 = 30,0003 50% 800 50×800 = 40,000
9.22800,4000,110)( w
xwX
Σ(w∙x) = 110,000Σw = 4,800
3.1 - 18
Example 12: New Diet ColaA recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
Area % Favored (x) Number Surveyed (w) w∙x1 40% 1,000 40×1000 = 40,0002 30% 3,000 30×3000 = 30,0003 50% 800 50×800 = 40,000
9.22800,4000,110)( w
xwXΣ(w∙x) = 110,000Σw = 4,800
The weighted percentage of people who liked the taste of the new diet cola is 22.9%.