1. Lesson 25 Finding measures of central tendency and dispersion

2. statistics Statistics is the branch of mathematics that involves the collection, analysis and comparison of numerical data. A measure of central tendency is used to represent the middle of a set of data

3. Measures of central tendency Mean ( average) of n numbers is the sum of the numbers divided by n, mean is denoted by "x bar" or "x" with a bar over it. Median of n numbers is the middle number when the numbers are written in order. If n is even, the median is the mean of the 2 middle numbers. Mode of n numbers is the number that appears most frequently in the list. There may be one mode, no mode, or more than one mode.

4. Finding measures of central tendency The following are Anne's grades for algebra quizzes: 18,15,20,16,17,19,19 Calculate the mean, median and mode mean = 124/7 = 17.7 Median= 18 Mode = 19

5. Measure of dispersion A measure of dispersion is a statistic that indicates how spread out, or dispersed, data values are. Three common measures of dispersion are the range, variance, and standard deviation

6. Measures of dispersion The range of a set of data is the difference between the largest and smallest data values. The variance of a data set is the average of the squared differences from the mean. The standard deviation measures, on average, how far away from the mean the data values are. The standard deviation, which is represented by the Greek letter sigma, is the square root of the variance and is calculated using the following formula

7. Finding measures of dispersion Find the range and standard deviation for the following sets of data: 5, 7, 12, 14, 17 Range = 17-5 = 12 Mean = 11 Standard deviation =

8. Find the range and standard deviation for the following sets of data 10,12,7,11,20,7,6,8,9 3,4,5,7,9 12,13,15,16,17

9. outlier An outlier is an item in a data set that is much larger or much smaller than the other items in the set. The presence of an outlier in a data set can have a misleading effect on the measures of central tendency and dispersion.

10. Examining the effect of an outlier Identify the outlier in the set. Then find the mean, median, mode, range, and standard deviation when the outlier is included and when it is not. 2,2,3,3,4,4,4,6,68 Outlier is 68 With outlier without outlier Range 66 4 Mode 4 4 Median 4 3.5 Mean 10.7 3.5 Stan dev 20.3 1.2

11. Box-and-whisker plot A box-and-whisker plot is a convenient way to organize data. The first quartile is the median of the lower half of the data set. The third quartile is the median of the upper half of the data set

12. Draw box-and-whisker plots to display the following data 31,29,28,20,35,22,32,22,32 32,44,42,34,40,34,33,30,46

13. Lab 5 Storing and plotting a list of data

14. P. 153 -storing a list of data Press STAT to open the statistics menu Press ENTER to edit the list Go to the L1 column and enter your data. Press Enter after each number. Go to L2 column and enter the data from the second data set Plotting data Turn on the plot feature by going to 2nd Y= which is stat plot Press ENTER to turn plot 1 on Pick the type of graph you want Graph

15. Lab 6- Calculating 1 and 2 variable statistical data

16. P. 178 Enter data sets into L1 and L2 as in lab 5 To calculate 1-variable statistics: Press STAT, then open the CALC menu select 1:1-var stats Input L1 by pressing 2nd 1

17. Calculating statistics for 2- variable data Press Stat, then go to Calc Go to 2:2-var stats Press enter It will analyze for values in L1 and L2 L1 will be referred to as x and L2 will be referred to as y

18. Box-and-whisker plot Press 2nd y= to open stat plot Press enter to turn plot on Choose box-and-whisker plot L1 should be displayed Move down to Freq Press Enter Go to zoom stat, Enter