1. Unit 3: Averages and Variations Week 6 Ms. Sanchez

2. MODE Mode: the value in a data set that occurs most frequently 5 3 7 2 4 4 3 2 4 8 3 4 3 1 2 2 1 4 5 2 3 5 2 3 5 3 1 = 2 2 = 6 3 = 7 4 = 5 5 = 4 6 = 0 7 = 1 8 = 1

3. MEDIAN Median: is the central value of an ordered distribution. The data set must be ordered from smallest to largest. Odd data set: the middle data value 4 3 2 4 8 3 4 3 1 2 2 Ordered data set: 1 2 2 2 3 3 3 4 4 4 8 Median: 3 Even data set: add both middle numbers divide by 2 10 9 6 8 1 12 3 2 Ordered data set: 1 2 3 6 8 9 10 12 Median:

4. MEAN Mean: is the average that uses the exact value of each entry. DATA SET 17 12 14 17 13 16 18 20 13

5. Vocabulary Terms Sample Mean:, is the mean of the sample data set. Population mean: is the mean of the entire population Resistant Measure: is one that is not influenced by extremely high or low data values Mean is NOT a resistant measure Mode is a resistant measure

6. Go to Google Classroom Work on the handout. Use the notes you just took This will be worth 5 stamps. Finish it by the end of the period. TURN IT IN!

7. RANGE In arithmetic: Is the difference between the smallest and the largest value in the data set. In statistics: The size of the smallest interval contains all the data and provides an indicator of statistical dispersion. EX. 2 3 4 7 8 9 10 12 15 Range: 15 - 2 = 13

8. Standard Deviation The standard deviation of a set of data is the average distance between the mean and the observed scores. A measure of how spread out are the numbers. Population Standard deviation: a measure of how spread out are the numbers in the population. Normally used in a Normal Distribution. Sample Standard deviation: a measure of how spread out are the numbers in the sample.

9. Finding standard deviation. Find the sample standard deviation of the data set. 2 3 4 5 6 8 10 10

10. Variance The average of the squared differences from the mean. The standard deviation squared. Population variance: Sample variance:

11. Find the sample variance 2 3 3 5 6 8 10

12. Coefficient of variation A percentage of the ratio of the standard deviation to the mean. It shows the extent of variability in relation to the mean of the population. * If a data set has a high percentage of CV then Using population mean and population standard deviation Using sample mean and sample standard deviation

13. Find the coefficient of variation 2 3 4 5 6 8 10 10

14. Quartiles Are a special type of percentile that divide the data into fourths: 1 st quartile “Q1” is the 25 th percentile 2 nd quartile “Q2” is the 50 th percentile (also known as the median 3 rd quartile “Q3” is the 75 th percentile

15. How to compute quartiles 1. Order the data from smallest to largest 2. Find the median, this is Q2. 3. Q1 (1 st quartile) is the median of the lower half of the data. It’s the median of the data falling BELOW the Q2. NOT including Q2 4. Q3 (3 rd quartile) is the median of the upper half of the data. It’s the median of the data falling ABOVE the Q2. NOT including Q2.

16. Finding the quartiles Calories in vanilla flavored ice cream bars. 342 377 319 439 295 239 197 131 151 209 151 190

17. Interquartile Range IQR = interquartile range. Is the difference between the Q3 and Q1 Q3 – Q1= IQR

18. 5 Number Summary Is a summary of data with the low and high data values, along with the quartiles Low Q1 Q2 Q3 Max

19. Boxplot Using the 5 number summary we can draw a diagram to represent a graphic sketch of the data collected.

21. Stem and leaf plot A plot where each data value is split into a leaf (the last digits) and a stem (the first digit). Data must be rearranged from smallest to largest. 32 = 3 (stem) 2 (leaf) 15 = 1 (stem) 2 leaf) 15, 16, 21 23, 23, 26, 26, 30, 32, 41

22. Create a stem leaf plot from the following set of data. Sam got his friends to do a long jump and got these different results. 2.3, 2.5, 2.7, 2.8, 3.2, 3.6, 4.5, 5.0

23. Skewedness in stem plots & histograms Develop a histogram from the stem leaf plot.