1 / 23

Chapter 4 Interpreting Histograms

Grouped Data are data presented in the form of a histogram, a frequency curve, an interval tally, or a similar display. An interval tally is a list of intervals and their frequency of scores. Chapter 4 Interpreting Histograms. use class midpoint of classes for variable x.

daryl-bright
Download Presentation

Chapter 4 Interpreting Histograms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Grouped Data are data presented in the form of a histogram, a frequency curve, an interval tally, or a similar display. An interval tally is a list of intervals and their frequency of scores. Chapter 4 Interpreting Histograms

  2. use class midpoint of classes for variable x Estimated value of Mean from a Frequency Table • m=class midpoint • f= frequency • N = total number

  3. m=class midpoint f = frequency N = total number m =average Estimated value of Standard Deviation from a Frequency Table

  4. ACT Scores Find the average mean and standard deviation Interval Frequency [32, 36) 3 [28,32) 6 [24,28) 12 [20,24) 10 [16,20) 8 [12,16) 2 Midpoint 34 30 26 22 18 14 Product 102 180 312 220 144 28 sum = 986 sum = 41 average mean is 986/41 = 24.04

  5. Interval Frequency [32, 36) 3 [28,32) 6 [24,28) 12 [20,24) 10 [16,20) 8 [12,16) 2 Midpoint 34 30 26 22 18 14 (mi - µ) 9.96 5.96 1.96 -2.04 -6.04 -10.04 (mi - µ)2 99.20 35.52 3.84 4.16 36.48 100.8 fi(mi - µ)2 297.6 213.13 46.099 41.616 291.85 201.16 sum = 1091.9

  6. (w •x) x =  w Weighted Mean A weighted mean of a group of scores is a mean computed in such a way that the frequency, or relative importance, of each score is taken into consideration Used when the data values are assigned different weights, such as grades received and the computation of a GPA.

  7. Find the Grade Point Average (4)(3.3)+3(3.0)+4(2.0)+5(2.6) = 43.2 43.2/16 = 2.7

  8. Find Liz’s Grade Point Average (2)(4.0)+4(3.33)+3(4.0)+2(.67) = 34.67 34.66/11 = 3.15

  9. The Empirical Rule (applies to bell-shaped distributions) 68% within 1 standard deviation 34% 34% x - s x x+s

  10. The Empirical Rule (applies to bell-shaped distributions) 95% within 2 standard deviations 68% within 1 standard deviation 34% 34% 13.5% 13.5% x - 2s x - s x x+s x+2s

  11. 0.1% The Empirical Rule (applies to bell-shaped distributions) 99.7% of data are within 3 standard deviations of the mean 95% within 2 standard deviations 68% within 1 standard deviation 34% 34% 2.4% 2.4% 0.1% 13.5% 13.5% x - 3s x - 2s x - s x x+s x+2s x+3s

  12. The Empirical Rule (applies to bell-shaped distributions) x

  13. 99.7% of data are within 3 standard deviations of the mean 95% within 2 standard deviations 68% within 1 standard deviation 34% 34% 2.4% 2.4% 0.1% 0.1% 13.5% 13.5% 80 100 130 70 90 110 120 IQ Scores have an average of 100 with a standard deviation of 10

  14. applies to distributions of any shape. the proportion (or fraction) of any set of data lying within K standard deviations of the mean  is always at least 1 - 1/K2, where K is any  positive number greater than 1. at least 3/4 (75%) of all values lie within 2  standard deviations of the mean. at least 8/9 (89%) of all values lie within 3  standard deviations of the mean. Chebyshev’s Theorem

  15. ACT Scores Interval Frequency [32, 36) 3 [28,32) 6 [24,28) 12 [20,24) 10 [16,20) 8 [12,16) 2 Midpoint 34 30 26 22 18 14 Product 102 180 312 220 144 28 average mean is 986/41 = 24.04  = 5.16

  16. What interval, centered around the mean in which approximately • 68% of the ACT scores? • 95% of the ACT scores? • 99% of the ACT scores? [18.9,29.2] 24.04  5.16 a. b. 24.04  2(5.16) [13.72,34.36] c. 24.04  3(5.16) [8.58,39.44] [8.58,36] Round to 36

  17. Using Chebyshev’s Theorem, what interval contains • 3/4 of the ACT scores? • 8/9 of the ACT scores? • 15/16 of the ACT scores? a. 24.04  2(5.16) [13.74,34.12] b. 24.04  3(5.16) [8.58,36] c. 24.04  4(5.16) [3.12,36]

  18. Estimating the mode a b L w L lower limit of the modal interval W is the modal interval width a and b are the differences in frequencies

  19. Estimating the median L lower limit of the median interval W is the median interval width N is the total number of scores F is the sum of the frequencies up to but not including the median interval f is the frequency of the median interval

  20. Find the estimated mode and median 9 8 7 5 4 2 4 6 8 10 = 4.333 = 5.714

  21. 11 9 8 6 5 0 2 4 6 8 10 Find the estimated mean, standard deviation, mode and median. Find an interval that would contain 95% of the data.

  22. Find the estimated mean, standard deviation, mode and median. Find an interval that would contain 95% of the data. 11 9 8 6 5 0 2 4 6 8 10 = 3.25 = 4.625

  23. Control Charts A control chart is a graph that can be used to indicate how a series of new scores compare with a historical based mean and standard deviation mean + 1 standard deviation mean mean - 1 standard deviation

More Related