1. Once we gather our data we need a way to represent our findings. One way to do this is through the use of a Frequency Distribution.

2. A frequency distribution or frequency table partitions data into classes or intervals. It shows how many data values are in each class. The classes or intervals are constructed so that data values can only appear in one class.

3. Once we gather our data we need a way to represent our findings. One way to do this is through the use of a Frequency Distribution. A frequency distribution or frequency table partitions data into classes or intervals. It shows how many data values are in each class. The classes or intervals are constructed so that data values can only appear in one class. To create a frequency table you will : a) decide how many classes or intervals you want to use. ( 5 to 15 classes are usually used )

5. EXAMPLE : Here is a table of mileage that workers travel for a one – way commute to their job. 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216

6. EXAMPLE : Here is a table of mileage that workers travel for a one – way commute to their job. 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Let’s use 6 data intervals

7. EXAMPLE : Here is a table of mileage that workers travel for a one – way commute to their job. 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Let’s use 6 data intervals The largest commuting value is 47 and the shortest is 1.

8. EXAMPLE : Here is a table of mileage that workers travel for a one – way commute to their job. 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Let’s use 6 data intervals

9. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216

10. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class Limits 1 9 17 25 33 41 Starting with the lowest value, I added the class width of 8 to each class…

11. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class Limits 1 – 8 9 – 16 17 – 24 25 – 32 33 – 40 41 - 48 Starting with the lowest value, I added the class width of 8 to each class… Now fill in the upper end of each class…notice their difference is 8 as well.

12. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTally 1 – 8 9 – 16 17 – 24 25 – 32 33 – 40 41 - 48 We are now going to go thru each data item and place it in its class…

13. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTally 1 – 8 9 – 16 I 17 – 24 25 – 32 33 – 40 41 - 48 We are now going to go thru each data item and place it in its class…

14. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTally 1 – 8 9 – 16 I 17 – 24 25 – 32 33 – 40 41 - 48 I We are now going to go thru each data item and place it in its class…

15. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTally 1 – 8 9 – 16 II 17 – 24 25 – 32 33 – 40 41 - 48 I We are now going to go thru each data item and place it in its class…

16. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTally 1 – 8 I 9 – 16 II 17 – 24 25 – 32 33 – 40 41 - 48 I We are now going to go thru each data item and place it in its class…

17. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTally 1 – 8 I 9 – 16 III 17 – 24 25 – 32 33 – 40 41 - 48 I We are now going to go thru each data item and place it in its class…

18. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTally 1 – 8 IIII IIII IIII 9 – 16 IIII IIII IIII IIII I 17 – 24 IIII IIII I 25 – 32 IIII I 33 – 40 IIII 41 - 48 IIII Continuing that process throughout the entire data list this is the result…

19. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequency 1 – 8 IIII IIII IIII 9 – 16 IIII IIII IIII IIII I 17 – 24 IIII IIII I 25 – 32 IIII I 33 – 40 IIII 41 - 48 IIII Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

20. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequency 1 – 8 IIII IIII IIII14 9 – 16 IIII IIII IIII IIII I 17 – 24 IIII IIII I 25 – 32 IIII I 33 – 40 IIII 41 - 48 IIII Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

21. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequency 1 – 8 IIII IIII IIII14 9 – 16 IIII IIII IIII IIII I21 17 – 24 IIII IIII I 25 – 32 IIII I 33 – 40 IIII 41 - 48 IIII Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

22. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequency 1 – 8 IIII IIII IIII14 9 – 16 IIII IIII IIII IIII I21 17 – 24 IIII IIII I11 25 – 32 IIII I 33 – 40 IIII 41 - 48 IIII Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

23. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequency 1 – 8 IIII IIII IIII14 9 – 16 IIII IIII IIII IIII I21 17 – 24 IIII IIII I11 25 – 32 IIII I6 33 – 40 IIII 41 - 48 IIII Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

24. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequency 1 – 8 IIII IIII IIII14 9 – 16 IIII IIII IIII IIII I21 17 – 24 IIII IIII I11 25 – 32 IIII I6 33 – 40 IIII4 41 - 48 IIII Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

25. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequency 1 – 8 IIII IIII IIII14 9 – 16 IIII IIII IIII IIII I21 17 – 24 IIII IIII I11 25 – 32 IIII I6 33 – 40 IIII4 41 - 48 IIII4 Next, we count the tally marks and fill in the frequency in which the data appears in that interval…

26. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequencyClass Midpt 1 – 8 IIII IIII IIII14 9 – 16 IIII IIII IIII IIII I21 17 – 24 IIII IIII I11 25 – 32 IIII I6 33 – 40 IIII4 41 - 48 IIII4

27. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequencyClass Midpt 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I21 17 – 24 IIII IIII I11 25 – 32 IIII I6 33 – 40 IIII4 41 - 48 IIII4

28. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequencyClass Midpt 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I11 25 – 32 IIII I6 33 – 40 IIII4 41 - 48 IIII4

29. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequencyClass Midpt 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I1120.5 25 – 32 IIII I6 33 – 40 IIII4 41 - 48 IIII4

30. Next we need to create our classes… 13471031620174042 7258211915317146 12451841611182312 6214137154612918 3415412836172427299 1426102437318161216 Class LimitsTallyFrequencyClass Midpt 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I1120.5 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5

31. Class LimitsTallyFrequencyClass Midpt 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I1120.5 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5 These basic frequency tables only show HOW MUCH data falls into each class. But sometimes we need to know what percentage of data falls into each class. This is called a Relative Frequency

32. Class LimitsTallyFrequencyClass Midpt 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I1120.5 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5

33. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I1120.5 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5 So let’s add another column to our table…

34. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.5 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I1120.5 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5 So let’s add another column to our table… There were 60 data items in our data list…

35. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.50.23 9 – 16 IIII IIII IIII IIII I2112.5 17 – 24 IIII IIII I1120.5 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5 So let’s add another column to our table…

36. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.50.23 9 – 16 IIII IIII IIII IIII I2112.50.35 17 – 24 IIII IIII I1120.5 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5 So let’s add another column to our table…

37. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.50.23 9 – 16 IIII IIII IIII IIII I2112.50.35 17 – 24 IIII IIII I1120.50.18 25 – 32 IIII I628.5 33 – 40 IIII436.5 41 - 48 IIII444.5 So let’s add another column to our table…

38. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.50.23 9 – 16 IIII IIII IIII IIII I2112.50.35 17 – 24 IIII IIII I1120.50.18 25 – 32 IIII I628.50.10 33 – 40 IIII436.5 41 - 48 IIII444.5 So let’s add another column to our table…

39. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.50.23 9 – 16 IIII IIII IIII IIII I2112.50.35 17 – 24 IIII IIII I1120.50.18 25 – 32 IIII I628.50.10 33 – 40 IIII436.50.07 41 - 48 IIII444.5 So let’s add another column to our table…

40. Class LimitsTallyFrequencyClass MidptRel. Freq. 1 – 8 IIII IIII IIII144.50.23 9 – 16 IIII IIII IIII IIII I2112.50.35 17 – 24 IIII IIII I1120.50.18 25 – 32 IIII I628.50.10 33 – 40 IIII436.50.07 41 - 48 IIII444.50.07 So let’s add another column to our table…