1. 10/17/2015Mrs. McConaughy1 Exploring Data: Statistics & Statistical Graphs During this lesson, you will organize data by using tables and graphs.

2. 10/17/2015Mrs. McConaughy2 Organizing Data Data- information, facts, or numbers that describe something A collection of data is easier to understand when it is organized in a table or graph. While there is no “best way” to organize such data; there are many good ways. This lesson illustrates several types of tabular and graphic representations. Tables, frequency distributions, line plots, histograms, circle graphs, and pictograms are all ways to represent data.

3. 10/17/2015Mrs. McConaughy3 REVIEW: Statistics  Statistics – numerical values used to summarize & compare sets of data (such as ERA in baseball).  Measures of Central Tendency – mean, median, & mode are the three “averages” which we will be using

4. 10/17/2015Mrs. McConaughy4 Mean – ( x ) average of n numbers (add all #s & divide by n) Median – the middle # when the #s are written in order from least to greatest or greatest to least. If there are two middle numbers, the median will be the average of those numbers. Mode – most frequently occurring number. NOTE: It is possible to have more than 1 mode or even no mode. Three “Averages”

5. 10/17/2015Mrs. McConaughy5 EXAMPLE: Find the mean, median, & mode of the following set of numbers: 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24. Mean - 445 13 Median – Put the numbers in order first! 17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48 Mode – most frequent! 40 is the mode.

6. 10/17/2015Mrs. McConaughy6 Measures of Dispersion Measures of Dispersion – tell how spread out the data are * Range – difference between the largest and smallest values. (for example: the range of the last example would be 48-17=31) * Standard Deviation - (σ – “sigma”) x 1, x 2, x 3, …, x n are the entries in the data set. n is the number of entries in the set x is the mean

7. 10/17/2015Mrs. McConaughy7 EXAMPLE: Find the standard deviation of the data from the first example.

8. 10/17/2015Mrs. McConaughy8 EXAMPLE: Box-and-whisker plots 0 10 20 30 40 50 Minimum value (17) Median (36) Maximum value (48) Lower Quartile – median of all numbers in the list to the left of the median (25+30)/2 = 27.5 Upper Quartile – median of all numbers to the right of the median (40+40)/2 = 40 Box Whisker

9. 10/17/2015Mrs. McConaughy9 Hints for making a box-and-whiskers plot:  Make sure data is in order from least to greatest.  Find the minimum value, median, maximum value, upper & lower quartiles.  Plot the points for this information below a number line.  Draw the box and whiskers.

10. 10/17/2015Mrs. McConaughy10 EXAMPLE: Frequency Distribution Title Goes Here IntervalTallyFrequency 0 to 9 0 10 to 19 l1 20 to 29 ll2 30 to 39 llll l6 40 to 49 llll4 Assign appropriate intervals that will include all data values in the set. Put a tally mark for each data value in the appropriate row. Count the number of tally marks and put the total in the last column.

11. 10/17/2015Mrs. McConaughy11 EXAMPLE: Histogram 65432106543210 TITLE HERE 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 LABEL HERE LABELLABELHEREHERELABELLABELHEREHERE Intervals Frequency Bars should be touching!

12. 10/17/2015Mrs. McConaughy12 Final Checks for Understanding 1.Give an example of a collection of data that you could organize using a box-and-whiskers plot. 2.Your classmates were asked to select their favorite type of music from these choices: classical, jazz, country, rock, and rap. How would you organize the results? 3.Which technique do you think is best suited to organize the results of a student council election?

13. 10/17/2015Mrs. McConaughy13 Homework Assignment: