1. 6th Grade Math Lab
MS Jorgensen
1A, 3A, 3B

2. Unit 1: Statistics and Graphical Representations

3. Measures of Central Tendency
This Week…
Measures of Center or
Measures of Central Tendency

4. Measures of Center
Measures of Central Tendency: A single number to serve as a representative value around which all the numbers in the set tend to cluster.
Sometimes it is referred to as a “middle” number of the data.
Three types of measures of central tendency:
Mean (average)
Median (middle)
Mode (most)

5. Mean (average)
The mean is the average. To determine the mean, add all the numbers in the set then divide by the number of items in the set.

6. Median (middle)
The median is the number in the middle when the numbers in the set are ordered from least to greatest. If there are two middle numbers, find the mean (average) of the two.

7. Mode (most)
The mode is the number, or numbers, that occur the most in the data set.

8. Shape and Distribution of Data
1) Symmetry
Symmetric Also ‘Fairly Symmetrical’
Skewed Left (negatively skewed)
Skewed Right (positively skewed)
2) Peaks
Single Peaked (unimodal)
Double Peaked (bimodal)
Multi Peaked (multimodal)
NOTE: Data have modes, dot plots have peaks

9. Symmetry in Data Sets
Symmetric distribution: the pattern of frequencies from a central point is nearly the same from the left and right. The left and right sides of the distribution are mirror images of one another.
Non-symmetric distribution: the patterns from a central point from the left and right are different.
Skewed to the left: If a distribution or tail extends much farther out to the left. The direction of skewness is on the side of the longer tail, in this case LEFT.
Skewed to the right: If a distribution or tail extends much farther out to the right. The direction of skewness is on the side of the longer tail, in this case RIGHT.

11. Skewed Left (negatively skewed)
Symmetric
Skewed Left (negatively skewed)
Tail
Skewed Right (positively skewed)
Tail

12. Peaks
Unimodal
Bimodal
Multimodal

13. More Distributions

14. Measures of Spread
-Range
-Interquartile Range (IQR)

15. Range
The range is the difference between the greatest and least numbers of the set .
31-2=29

16. IQR- Interquartile Range
The interquartile range is a measure of variability, based on dividing a data set into quartiles.
Quartiles are the values that divide a list of numbers into quarters.
Quartile 1, Q1
Quartile 2, Q2
Quartile 3, Q3
Quartile 4, Q4

17. Finding IQR 1. Put the list of numbers in order
2. Then cut the list into 4 equal parts
Sometimes a "cut" is between two numbers ... the Quartile is the average of the two numbers.
3. The Quartiles are at the “cuts”
The Interquartile Range is from Q1 to Q3:
To calculate it just subtract Quartile 1 from Quartile 3 (Q3-Q1)