Download 8-4: Use the Mean Remembering: How to find the mean? Add to find

8-4: Use the Mean
Remembering: How to find the mean?
Add to find the sum of the numbers, then divide the sum by the number of values.
Example:
In Ms. Dixon’s science class, the mean of four quiz scores and a final test score determine the quarterly grade.
During the first quarter, Katelyn’s four quiz scores were 95, 99, 86, and 94.
a) What is the sum of Katelyn’s four quiz scores?
Sum of 4 = 95 + 99 + 86 + 94 = 374
b) What must the sum of Katelyn’s five scores be for her to average 90 or more on all four quizzes and the
test?
Sum of all 5 must total
?
to average 90 or more? 90 + 90 + 90 + 90 + 90 = 450 ÷ 5 = 90
c) What is the minimum score Katelyn must earn on the final test to have an average score of at least 90
for the quarter?
An average score of 90 requires 450 points. Since Katelyn has already earned 374 points, she needs at
least a score of 76 because 450 – 374 = 76.
8-5: The Mean as a Balance Point
The balance point is the mean.
Unbalanced
Balanced
Un-level in a consistent way. Does un-leveling the data change the mean? No, the mean does not change.
5 + 5 + 5 + 5 + 5 = 25
3 + 5 + 5 + 5 + 7 = 25
25 ÷ 5 = 5 (Mean)
25 ÷ 5 = 5 (Mean)
Find the balance point.
a) What number is the exact center on the
plot? 5
b) What is the mean (balance point)?
2 + 2 + 8 = 12 ÷ 3 = 4 Mean = 4
**The exact center of a dot plot does not always represent the mean and the balance point of the data.
**Un-leveling data by shifting it to the left will move the balance point to the left and decrease the mean.
**Un-leveling data by shifting it to the right will move the balance point to the right and increase the mean.
8-6: Find and use the Median
Median: a single number that summarizes the center of a set of numerical data.
Symmetric: a dot plot is symmetric when the shape of the data on one side of the line of symmetry is the
same as the shape of the data on the other side.
Line of symmetry
Example 1:
Find the Median: 37 22 10 21 46
Step 1: Order the numbers from least to greatest.
10 21 22 37 46
Step 2: Cross off the smallest and biggest
numbers.
10 21 22 37 46
Step 3: Continue crossing off the smallest and
biggest numbers until you reach the center.
10 21 22 37 46
Step 4: The median is the middle number.
Median = 22
Example 2:
Find the Median: 7 4 5 1 9 6 8 9
Step 1:
1 4 5 6 7 8 9 9
Step 2/3:
1 4 5 6 7 8 9 9
Step 4: When two numbers are in the middle you
need to find the mean (average) of the two.
1
6 + 7 = 13 ÷ 2 = 6.5 or 62