1. Mean, Median, and Mode of Ungrouped Data Section 2.5

2. Mean - Ungrouped

3. Median - Ungrouped No formula – BUT, we do use a “position locator” formula to show us where to begin to find the median in the cumulative frequency column. (cf) Position Locator:

4. Cumulative Frequency - cf The cumulative frequency is a column which keeps a running total of the frequencies. Ex: fcf 10 2030 60 40100 n =100

5. Mode Find the number with the greatest frequency (f) and read the “x” value. This is the mode of the set or the value that occurs the most often.

6. Example Find the mean, median, and mode of the following data. xf 13 28 35 44 52 61 71 n=24

7. Put “x” in L1 and “f” in L2.

8. In L3 set a formula for

9. You should see this….L3 shows (f)(x).

10. On your chart – not in calculator – add a column for cf. xffxcf 1333 281611 351516 44 20 521022 61623 71724 n=2473

11. Find the mean….

12. Find the median…… n/2 = 24/2 = 12 Locate the class containing the 12 th value in the set in the cumulative frequency column.

13. The 12 th position is after 11 th and before 16 th ……… xffxcf 1333 281611 351516 44 20 521022 61623 71724 n=24

14. Now, read the x value that corresponds to the 12 th position…. The median is 3. xffxcf 1333 281611 351516 44 20 521022 61623 71724 n=24

15. Find the mode……. Locate the highest frequency and read the x value that corresponds. NOTE: The mode is not the frequency, it is the x that corresponds to that frequency.

16. The largest frequency is “8”… xffxcf 1333 281611 351516 44 20 521022 61623 71724 n=24

17. The mode is 2. xffxcf 1333 281611 351516 44 20 521022 61623 71724 n=24

18. Now, you try……… Find the mean, median, and mode of the following set of data. xf 12.56 24.510 36.513 48.58 60.55 72.56 84.52 50

19. This is the chart you should have…….. xffxcf 12.56756 24.51024516 36.513474.529 48.5838837 60.55302.542 72.5643548 84.5216950 2089

20. The mean……

21. The median……. n/2 = 50/2 = 25 xffxcf 12.56756 24.51024516 36.513474.529 48.5838837 60.55302.542 72.5643548 84.5216950 2089

22. The mode…….. xffxcf 12.56756 24.51024516 36.513474.529 48.5838837 60.55302.542 72.5643548 84.5216950 2089

23. Now, use the calculator….. Put “x’s” in L1 and frequencies in L2. Press “Stat”, Calc, One-Var stats, L1, L2 and then enter. The next slide will show the keystrokes necessary.

24. Keystrokes….

25. Screen shows mean. Median can be found as you scroll down…..

26. Variance and St. Deviation – Ungrouped Section 2.5

27. Variance Formula - Ungrouped

28. Standard Deviation Formula….

29. Example - Ungrouped Find the variance and standard deviation of the set. xf 54 63 79 86 92 101 n=25

30. Calculator Lists……. Put x’s in L1 and f’s in L2. Then set a formula to find f (x).

31. Finding f times x squared…. Set a formula in L4

32. This is what your columns should look like…… xffxf (x squared) 5420100 6318108 7963441 8648384 9218162 101 100 n=251771295

33. Find the variance.

34. Find the standard deviation.

35. Now you try… Find the variance and standard deviation of the set. xf 102 113 126 137 145 151 n=24

36. Your lists should look like this….. xffxf (x squared) 10220200 11333363 12672864 137911183 14570980 151 225 n=243013815

37. Find variance.

38. Find the standard deviation.

39. Calculator Only….. Put x’s in L1 and f’s in L2. Press Stat, Calc, One-var stats, L1,L2 enter

40. Homework Make sure that you do all the homework BY HAND using the columns. After you finish, you can check your answers using your calculator.