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Mean, Median, Mode, and Midrange of Grouped Data

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

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Mean, Median, Mode, and Midrange of Grouped Data

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  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.

  8. Here is the list you should have……

  9. Mean……

  10. Median….. • n/2 = 20/2 = 10

  11. Plug values into formula….

  12. Mode and Midrange…… • The mode is 21-26. • Midrange =

  13. Now you try………. • Find the mean, median, and mode of the following set.

  14. Your finished list…….

  15. Mean……

  16. Median…….

  17. Mode…….. • The mode is 69-72.

  18. Midrange…….. • The midrange = (63 + 78)/2 = 70.5

  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.

  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……

  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.

  32. Here are the lists……

  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.

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