1. Mean, Median, Mode, and Midrange of Grouped Data
Section 2.5

2. Grouped Data……
You must add one more column than you did using ungrouped data.
You now need a midpoint column.
The symbol for the midpoint is

3. Formulas……Mean
Mean

4. Median
There IS a formula to find the median using grouped data.

5. Mode……
Find the greatest frequency and read across the chart until you see the class that corresponds to it.
Your answer will be the entire interval.

6. Midrange…..
Add the lowest number in the first row to the highest number in the last row.
Divide that answer by 2.

7. Example….. Find the mean, median, and mode of the set of grouped data.
6-11 1
11-16 2
16-21 3
21-26 5
26-31 4
31-36
36-41
n=20

8. Here is the list you should have……x f
midpoint
f x midpoint cf
6-11 1
8.5
11-16 2
13.5 27 3
16-21
18.5
55.5 6
21-26 5
23.5
117.5 11
26-31 4
28.5
114 15
31-36
33.5
100.5 18
36-41
38.5 77 20
500

9. Mean……

10. Median…..
n/2 = 20/2 = 10 x f
midpoint
f(midpoint) cf
6-11 1
8.5
11-16 2
13.5 27 3
16-21
18.5
55.5 6
21-26 5
23.5
117.5 11
26-31 4
28.5
114 15
31-36
33.5
100.5 18
36-41
38.5 77 20
500

11. Plug values into formula….

12. Mode and Midrange…… The mode is 21-26. Midrange = 6-11 1 8.5 11-16 2x f
midpoint
f(midpoint) cf
6-11 1
8.5
11-16 2
13.5 27 3
16-21
18.5
55.5 6
21-26 5
23.5
117.5 11
26-31 4
28.5
114 15
31-36
33.5
100.5 18
36-41
38.5 77 20
500

13. Now you try………. Find the mean, median, and mode of the following set.x f
63-66 2
66-69 4
69-72 8
72-75 5
75-78
n=21

14. Your finished list……. 63-66 2 64.5 129 66-69 4 67.5 270 6 69-72 8 70.5x f
midpoint
f(midpoint) cf
63-66 2
64.5
129
66-69 4
67.5
270 6
69-72 8
70.5
564 14
72-75 5
73.5
367.5 19
75-78
76.5
153 21
n=21
1483.5

15. Mean……

16. Median…….

17. Mode…….. The mode is 69-72. x f midpoint f(midpoint) cf 63-66 2 64.5
129
66-69 4
67.5
270 6
69-72 8
70.5
564 14
72-75 5
73.5
367.5 19
75-78
76.5
153 21
n=21
1483.5

18. Midrange…….. The midrange = (63 + 78)/2 = 70.5 x f midpointcf
63-66 2
64.5
129
66-69 4
67.5
270 6
69-72 8
70.5
564 14
72-75 5
73.5
367.5 19
75-78
76.5
153 21
n=21
1483.5

19. Range, Variance and St. Deviation – Grouped
Section 2.5

20. Grouped Data……
Variance Formula

21. Standard Deviation

22. Range…..
High number in last row minus low number in first row.

23. Example…… Find the variance, standard deviation, and range of the set.
2-8 12
8-14 4
14-20 6
20-26 22
26-32 8
n=52

24. Calculator Steps……
Put lower boundaries in L1 and upper boundaries in L2. Put frequencies in L3. Set a formula for midpoint in L4.

25. Find f times midpoint by setting a formula in L5.

26. Find f times midpoint squared in L6 by setting a formula.

27. Your lists should look like this……x f
midpoint
f (midpoint)
f ( midpoint sq)
2-8 12 5 60
300
8-14 4 11 44
484
14-20 6 17
102
1734
20-26 22 23
506
11638
26-32 8 29
232
6728
n=52
944
20884

28. Find the variance.

29. Find the standard deviation.

30. Range = High - Low
Range = 32 – 2 = 30

31. Example……
Find the mean, median, mode, midrange, range, variance, and st. deviation of the data set. x f 5 9 7 3 2

32. Here are the lists…… x f
midpoint
f x midpoint
f x mp squared cf 5
12.5
62.5
781.25 9
17.5
157.5
2756.3 14 7
22.5
3543.8 21 3
27.5
82.5
2268.8 24 2
32.5 65
2112.5 26
n=26
525

33. Mean:

34. Median……

35. Mode……
Greatest Frequency is 9.
Mode = 15-20

36. Midrange……

37. Range……

38. Variance……

39. St. Deviation……

40. Homework…….
Find the measures of center and variation for the grouped data on HW3.