1. Statistical Reasoning for everyday life
Intro to Probability and Statistics
Mr. Spering – Room 113

2. 4.1 Measures of Central Tendency
MEAN:
The mean is most commonly called the average. It is found by finding a sum of set of values and then dividing by the number of data within that set.
MEAN =

3. 4.1 Measures of Central Tendency
MEAN:
Find the mean of the following data set.
15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13.
MEAN =
SUM: = 102
MEAN = 102 ∕11 =
≈ 9.3

4. 4.1 Measures of Central Tendency
MEDIAN:
The median is the value exactly in the middle of the data set (possibly halfway between the middle values of the number of values is even). It is found by first sorting the data ordinally, according to data values and finding the middle value.

5. 4.1 Measures of Central Tendency
MEDIAN:
Find the median of the following data set.
15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13.
Sort data:
1, 1, 7, 9, 9, 10, 11, 13, 13, 13, 15
Find the middle number:
MEDIAN: 10

6. 4.1 Measures of Central Tendency
MODE:
Most common number in a distribution.
{Data set may have one mode, more than one mode, or no mode}

7. 4.1 Measures of Central Tendency
MODE:
Find the mode of the following data set.
15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13.
Most repeated number?
MODE = 13

8. 4.1 Measures of Central Tendency
Rounding Rule:
State your answers with one more decimal place of precision than is found in the raw data.
i.e. Find the mean of 2, 3, 5 is 3⅓, which is 3.3
When in doubt at any other time in class round to the nearest one hundredth of questioned value.
i.e. Find index value of reference value 0.15 compared to new value of 1.455
970.00

9. 4.1 Measures of Central Tendency
OUTLIER:
An outlier in a data set is a value that is much higher or lower than almost all other value.
i.e. Is there an outlier?
Quiz grades: 9, 9, 9, 9, 8, 9, 9, 7, 10, 10, 11, 10, 8, 9, 9, 10, 3, 7, 8, 8, 9, 10
YES: 3 is much lower than most of the data

10. 4.1 Measures of Central Tendency
How does an outlier affect Central Tendency?
Measure
Takes every value into account?
Affected by Outliers?
Advantages
MEAN
Yes
Commonly understood, works well with many statistical methods
MEDIAN
No (remember must count values) No
When there are outliers may be more representative of an “average” than the mean
MODE
Most appropriate for data at the nominal level of measurement

11. 4.1 Measures of Central Tendency
WEIGHTED MEAN:
A weighted mean accounts for variation in the relative importance of data values. Each data value is assigned a weight, and the weighted mean is:
Weighted Mean =

12. 4.1 Measures of Central Tendency
WEIGHTED MEAN:
Weighted Mean =
i.e. Your class average!
Classwork/Homework/Participation 20%
Quizzes/Tests 80%
For example:
Classwork/Homework/Participation 14/20 = 70.0%
Quizzes/Tests 45/50 = 90.0%
Final Average: 0.20(70.0) (90.0) = 86%

13. 4.1 Measures of Central Tendency
Algebraic Form
Definition
Sum of all values
Mean of an entire population.
Weighted Mean
Means with More Mathematical Notation

14. 4.1 Measures of Central Tendency
GOOD LUCK !!!!!!!

15. 4.1 Measures of Central Tendency
What are the mean, median, and mode of the data in the following sample?
7, 16, 1, 16, 13, 16, 11, 16, 9, 15
Mean: 12
Median: 14
Mode: 16

16. 4.1 Measures of Central Tendency
HW: pg 154 # all and odd