1. Frequency Distribution Objectives: Create Frequency Distributions Analyze Frequency Distribution

2. What is a Frequency Distribution? Allows us to understand and interpret the nature of the distribution of a data set. Shows how data is partitioned among classes by listing the classes along with the number of data values in each.

3. PULSE RATES (BEATS PER MINUTE) of FEMALES 767288607268806468 80766872967268726480 648076 80104886076 72 8880607288 12464

4. Creating a Frequency Distribution Table Lower Class Limits: smallest numbers that can belong to the different classes Upper Class Limits: largest numbers... Class Boundaries: numbers used to separate the classes, but w/out the gaps created by class limits Class Midpoints: values in the middle of the classes Class width: difference b/w 2 consecutive lower/upper class boundaries

5. Procedure: Determine the number of classes –W–Will either be given or found by – ALWAYS ROUND UP!

6. Calculate the Class Width Round up for convenience

7. Lower Class Limit Select either the lowest data value or a convenient value below the minimum as the first lower class limit.

8. Cont... Using the class width and the first lower class limit begin listing the lower class limits in a vertical column by adding the class width.

9. Adding the upper class limits Identify the corresponding upper class limits to each class making sure that the classes do not overlap

10. Finish by... Taking the total values in each class and listing them is column number 2

11. Things to watch out for: Confusing the class width and the class boundaries –Class width is the difference between lower or upper class limits! Make sure you include all classes, even those with 0 data values. The sum of column 2 should be the # of values in data set

12. Example using Female Pulse Rates Step 1: Find total # of classes – n=40 Round up: There are 7 classes Pulse RateFrequency

13. Calculate Class Width

14. Begin filling in table Choose 60 as the first lower class limit because it is both the minimum value and a convenient value Add the class width and record in following rows

15. Pulse RateFrequency 60- 70- 80- 90- 100- 110- 120-

16. Identify corresponding UCL Make sure you leave no gaps where numbers would fit in. Pulse RateFrequency 60-69 70-79 80-89 90-99 100-109 110-119 120-129

17. Finish by... Calculating frequency for each class All values should be included totals should match up! Pulse RateFrequency 60-6912 70-7914 80-8911 90-991 100-1091 110-1190 120-1291

18. Relative Frequency Tables Same Classes Sum must be close to 1

19. Relative frequency distribution tables Pulse RateRelative Frequency 60-6930% 70-7940% 80-8927.5% 90-992.5% 100-1092.5% 110-1190 120-1292.5%

20. Cumulative Frequency Replace lower class limits with “less than...” Add each cell to previous cells Pulse RateFrequency Less than 7012 Less than 8026 Less than 9037 Less than 10038 Less than 11039 Less than 12039 Less than 13040

21. Interpreting Frequency Distributions Normal Distribution (Bell Curve) within a frequency distribution table: Frequencies start low, increase in frequency, then return to low. Distribution is approximately symmetric

22. IQ Scores of 1000 Adults IQ scoreFreqNormal Dist 50-6924frequencies start low... 70-89228 90-109490increase to maximum... 110-129232 130-14926decrease to be come low again. Relatively symmetric

23. Last Digits of Female Pulse Rates Last digit Freq 09 10 28 30 46 50 67 70 810 90

24. Randomly Selected Pennies Wt. (grams) of penniesFrequency 2.40-2.4918 2.50-2.5919 2.60-2.690 2.70-2.790 2.80-2.890 2.90-2.992 3.00-3.0925 3.10-3.198