Mean Median Mode and Midrange of Grouped Data

Mean, Median, Mode, and Midrange of Grouped Data Section 2. 5

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

Formulas……Mean n Mean

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

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

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

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

Here is the list you should have…… x f midpoint f x midpoint cf 6 -11 11 -16 16 -21 1 2 3 8. 5 13. 5 18. 5 27 55. 5 1 3 6 21 -26 26 -31 31 -36 36 -41 5 4 3 2 23. 5 28. 5 33. 5 38. 5 117. 5 114 100. 5 77 11 15 18 20 20 500

Mean……

Median…. . n n/2 = 20/2 = 10 x f midpoint f(midpoint) cf 6 -11 1 8. 5 1 11 -16 2 13. 5 27 3 16 -21 3 18. 5 55. 5 6 21 -26 5 23. 5 117. 5 11 26 -31 4 28. 5 114 15 31 -36 3 33. 5 100. 5 18 36 -41 2 38. 5 77 20 20 500

Plug values into formula….

Mode and Midrange…… n n The mode is 21 -26. Midrange = x f midpoint f(midpoint) cf 6 -11 1 8. 5 1 11 -16 2 13. 5 27 3 16 -21 3 18. 5 55. 5 6 21 -26 5 23. 5 117. 5 11 26 -31 4 28. 5 114 15 31 -36 3 33. 5 100. 5 18 36 -41 2 38. 5 77 20 20 500

Now you try………. n Find the mean, median, and mode of the following set. x f 636 6 2 666 9 4 697 2 8 727

Your finished list……. x f midpoint f(midpoint) cf 63 -66 66 -69 2 4 64. 5 67. 5 129 270 2 6 69 -72 72 -75 75 -78 8 5 2 70. 5 73. 5 76. 5 564 367. 5 153 14 19 21 n=21 1483. 5

Mean……

Median…….

Mode……. . n The mode is 69 -72. x f midpoint f(midpoint) cf 63 -66 2 64. 5 129 2 66 -69 4 67. 5 270 6 69 -72 8 70. 5 564 14 72 -75 5 73. 5 367. 5 19 75 -78 2 76. 5 153 21 n=21 1483. 5

Midrange……. . The midrange = (63 + 78)/2 = 70. 5 n x f midpoint f(midpoint) cf 63 -66 2 64. 5 129 2 66 -69 4 67. 5 270 6 69 -72 8 70. 5 564 14 72 -75 5 73. 5 367. 5 19 75 -78 2 76. 5 153 21 n=21 1483. 5

Range, Variance and St. Deviation – Grouped Section 2. 5

Grouped Data…… n Variance Formula

n Standard Deviation

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

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

Calculator Steps…… n Put lower boundaries in L 1 and upper boundaries in L 2. Put frequencies in L 3. Set a formula for midpoint in L 4.

n Find f times midpoint by setting a formula in L 5.

n Find f times midpoint squared in L 6 by setting a formula.

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 944 20884 n=52

n Find the variance.

n Find the standard deviation.

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

Example…… n Find the mean, median, mode, midrange, variance, and st. deviation of the data set. x f 10 - 1 5 5 15 - 2 0 9 20 - 2

Here are the lists…… x f midpoint f x mp squared cf 10 - 15 5 12. 5 62. 5 781. 25 5 15 - 20 9 17. 5 157. 5 2756. 3 14 20 - 25 7 22. 5 157. 5 3543. 8 21 25 - 30 3 27. 5 82. 5 2268. 8 24 30 - 35 2 32. 5 65 2112. 5 26 525 11462. 5 n=26

Mean:

Median……

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

Midrange……

Range……

Variance……

St. Deviation……

Homework……. n Find the measures of center and variation for the grouped data on HW 3.