1. Warm-Up 1.

2. Warm-Up
Use the data to make a frequency table, and make a histogram for the data. 2. strikeouts per game: What makes the data display misleading? List everything you find.

3. Measures of Central Tendency

4. The Arithmetic Mean
This is the most popular and useful measure of central location
Sum of the observations
Number of observations
Mean =
This is often called the average.

5. Useful Notation
x: lowercase letter x - represents any measurement in a sample of data.
n: lowercase letter n – number of measurements in a sample
∑: uppercase Greek letter sigma – represents sum
∑x: - “add all the measurements in a sample.
: – lowercase x with a bar over it – denotes the sample mean
µ: lowercase Greek letter mu – denotes the population mean

6. The Arithmetic Mean Sample mean Population mean Sample size
Population size

7. Median- is the middle value in a data set when the values are arranged in order
Arrange the data values in order of size, least to greatest.
If the number of data values is odd, the median is the middle of the data set.
If the number of data values is even, the median is the average of the two middle data values.

8. Mode- is the data value that occurs the most times.
3 types of modes
1. no mode
2. one mode
3. more than one mode

9. The mean, median and mode are all measures of central tendency.

10. Which measure of central tendency is more accurate?
When data is skewed, you will be able to use the median to get a better representation of data.
So you eliminate any extremely high values or extremely low values. The median is not affected by these outliers.

11. Which measure of central tendency is more accurate?
If we can say the data is symmetric, we can say the mean is the best.
Although there is a high value, it is balanced out by a low value.

12. Mean and Median Comparisons
If the data is symmetric, the mean and the median are approximately the same.
If the data is skewed to the right, the mean is larger than the median.
If the data is skewed to the left, the mean is smaller than the median.

13. Outlier- is a data value that is much greater or less than the other values in the set.
Range- is the difference between the highest data value and the lowest data value (variability).

14. The range is a measure of spread/dispersion which describes how spread out the values in a data set are.

15. Examples The following bowling scores were collected. 104 189 117 109
113
136
Rearrange scores from least to greatest.
Mean
Median
Mode
Range
Outliers

16. 3. The cost of different belts at an online store. $15.99 $5.25 $6.95
Rearrange scores from least to greatest.
$15.99
$5.25
$6.95
$6.25
$8.85
$7.45
Mean
Median
Mode
Range
Outliers

17. Finding a Data Value-Example
Your grades on three exams are 80, 93, and 91. What grade do you need on the next exam to have an average of 90 on the four exams?

18. You Try:
Your grades on three exams are 85, 94, and 89. What grade do you need on the next exam to have an average of 92 on the four exams?

19. Example The closing prices, in dollars, of two stocks for the first five days in February are shown below. What are the range and mean of each set of data? Use the results to compare the data sets. S A: 25, 30, 30, 47, 28 S B: 34, 28, 31, 36, 31

20. You Try The closing prices for the same days, in dollars, of Stock C were 7, 4, 3, 6 and 1. the closing prices, in dollars, of Stock D were 24, 15, 2, 10, and 5. what are the range and mean of each set of data?

21. Matching/Worksheet