1 Message to the user... The most effective way to use a PowerPoint slide show is to go to “SLIDE SHOW” on the top of the toolbar, and choose “VIEW SHOW” from the pull down menu. OR, using the shortcut toolbar on the bottom left, choose the rightmost icon (“SLIDE SHOW”) Use the spacebar, enter key or mouse to move through the slide show. Use the backspace key to undo the last animation on a slide TEACHERS : If using this show as part of a lecture, it is helpful to go to “PRINT” in the “FILE” menu and use the drop down menu at the bottom left: “PRINT WHAT.” For some shows, printing the “OUTLINE VIEW” will be helpful; as well as printing particular slides to use as handouts. (Many shows will include sound… you may want to turn on your speakers!) Revised 2002 Statistics Show #1 of 3

2 Statistics... Median, Mean, Range Quartiles 5-Number Summary

3 Arithmetic(numeric) Data Analysis A. Measures of Center FIRST… RANK the data: list it in order (usually) smallest -- largest 1. Median (M) of a distribution of n values: is found in the (n+1)/2 place in the list. (It is sometimes referred to as the 50th percentile) If n (the number of values in the list) is odd, then the median is an actual value in the list. If n is even, then the median is the average of the 2 middle values. (It might not be an actual value in the list)

4 Arithmetic(numeric) Data Analysis A. Measures of Center (ex#1) Given the following set of data, find the median (M) There are 15 values in the list (n=15) The POSITION of the median is: (15+1)/2 = 8th position The value of the median, M=25 M

5 Arithmetic(numeric) Data Analysis A. Measures of Center (ex#2) Given the following set of data, find the median (M) There are 4 values in the list (n=4) The POSITION of the median is: (4+1)/2 = 2.5th position The value of the median, M=(19+21)/2 = 40/2 = 20 M =20

6 Arithmetic(numeric) Data Analysis A. Measures of Center 2. Mean (x) of a distribution of n values: is the arithmetic average of the n values. (the sum of the values)/n (ex#2) Find the mean (x) of the 4 values: so, n=4 and the mean: x = ( )/4 x = 78/4 = 19.5

7 Arithmetic(numeric) Data Analysis B. Measures of SPREAD 1. RANGE: the difference described by subtracting: highest - lowest value Also sometimes expressed by stating “highest value” to “lowest value” (ex#1) The RANGE of the 15 values is:  = 15 units The values range from 17 to 32

8 Arithmetic(numeric) Data Analysis B. Measures of SPREAD 2. QUARTILES: used to measure the spread of the data when the MEDIAN is the measure of center. a. Rank the data b. Examine the data to the left of M and find their median call this median Q1 the first quartile (also called the 25th percentile) (ex#1) The 7 values to the left of M are: since n = 7 for this set of data, its MEDIAN (Q1) will be found in the: (7+1)/2 = 4th position So Q1 = 21 Q1

9 Arithmetic(numeric) Data Analysis B. Measures of SPREAD 2. QUARTILES c. Do the same thing for those values to the RIGHT of M Find their median Call it Q3 the third quartile (also called the 75th percentile) (ex#1) The 7 values to the right of M are: since n = 7 for this set of data, its MEDIAN (Q3) will be found in the: (7+1)/2 = 4th position So Q3 = 30 Q3

10 Arithmetic(numeric) Data Analysis B. Measures of SPREAD 2. QUARTILES (ex#1) d. Now the data is split into 4 equal parts (quarters) The QUARTILES are those MEDIANS found in steps (b) and (c) Q3MQ1

11 Arithmetic(numeric) Data Analysis B. Measures of SPREAD 3. 5-number summary: to describe the spread of the data about the MEDIAN is a list of the following values (in order from lowest to highest)... LOWESTQ1MQ3 HIGHEST LOWEST Q1 M Q3 HIGHEST (ex#1) The 5-Number Summary for this set of data is: From this we can tell a lot about the set of data, without seeing all 15 values.

12 Arithmetic(numeric) Data Analysis B. Measures of SPREAD (ex#1) The 5-Number Summary for this set of data is: Without seeing all of the data, we know: 50% of the data is 25 or less 25% of the data is 21 or less 75% of the data is 30 or less The data values range from 17 to 32 etc... BOX PLOT: a picture of a 5-number summary. A box spans the quartiles with a line to mark the median Whiskers extend to the high and low values.

13 Arithmetic(numeric) Data Analysis B. Measures of SPREAD (ex#1) 1. BOX PLOT : a picture of a 5- number summary. A box spans the quartiles with a line to mark the median Whiskers extend to the high and low values.  The 5 # Summary is The box plot can be vertical or horizontal

14 Using the 5# Summary to describe the spread of the data... The 5# Summary is used with the MEDIAN and QUARTILES. It gives you useful information about the original set of data without seeing the entire list. It is an especially useful description of data that is skewed or has outliers.

15 End of show #1 Going on?... Statistics Show # 2: Mean & Standard Deviation REVISED 2002 Prepared by Kimberly Conti, SUNY Fredonia Suggestions and comments to: