1. Statistics Class 3 Jan 30, 2012

2. Group Quiz 2 1. The Statistical Abstract of the United States includes the average per capita income for each of the 50 states. When those 50 values are added, then divided by 50, the result is $29,672.52. Is $ 29,672.52 the average per capita income for all individuals in the United States? Why or why not? 2. A classroom consists of 36 students seated in six different rows, with six students in each row. The instructor rolls a die to determine a row, then rolls the die again to select a particular student in the row. This process is reapeated until a sample of 6 students is obtained. Does this sampling plan result in a ran d om sample? Simple random Sample? Explain.

3. Frequency Distributions We recorded the pulses of 40 women. Here it is! 76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64 This data is hard to make sense of so we (you) are going to organize it using a Frequency Distribution (Table)

4. Frequency Distributions A frequency Distribution shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories. Lower class limits are the smallest numbers that can belong to the different classes. Upper class limits are the largest numbers that can belong to the different classes. Class boundaries are the numbers used to separate the classes, but without the gaps created by class limits

5. Frequency Distributions Class midpoints are the values in the middle of the classes. Class width is the difference between two consecutive lower class limits.

6. Procedure for constructing a frequency Distribution. 1. Determine the number of classes. 2. Calculate the class width. class width= (max data value-min data value)/number of classes. 3. Choose either the min data value or convenient value below the min data value as the first lower class limit. 4. Using the first lower class limit and class width, list the other lower class limits. Do this vertically and add in the upper class limits 5. Tally up the data values in each class.

7. Example 1 Frequency table by hand. 76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64 1. Lets Have 7 classes. 2. Find the width.

8. Example 1 Frequency table by hand. 76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64 1. Lets Have 7 classes. 2. Find the width. 124-60= 64 64/7=9.14

9. List the min data value or convenient data value

10. 60 List the lower values

11. 60 70 List the lower values

12. 60 70 80 90 100 110 120 Add in the upper limit values

13. 60-69 70-79 80-89 90-99 100-109 110-119 120-129 Tally Ho!

14. 76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64

15. 60-6912 70-79 80-89 90-99 100-109 110-119 120-129 Tally Ho!

16. 76 64 72 80 88 76 60 76 72 76 68 80 80 104 64 88 68 60 68 76 80 72 76 72 68 88 72 80 96 60 72 72 68 88 72 88 64 124 80 64

17. 60-6912 70-7914 80-89 90-99 100-109 110-119 120-129 Tally Ho!

18. Pulse RateFreq 60-6912 70-7914 80-8911 90-991 100-1091 110-1190 120-1291

19. Relative Frequency In a relative frequency the frequency is replaced with a relative frequency (proportion) or a percentage frequency (percent). Relative frequency=class frequency/sum of all frequencies Percentage freq=(class freq/sum of all freq)*100%

20. Pulse RateRelative Frequency 60-6912/40 70-7914/40 80-8911/40 90-991/40 100-1091/40 110-1190/40 120-1291/40 Change into a relative frequency

21. Pulse RateRelative Frequency 60-6912/40=0.3 70-7914/40=0.35 80-8911/40=0.27 90-991/40=0.025 100-1091/40=0.025 110-1190/40=0 120-1291/40=0.025 Change into a relative frequency

22. Pulse RateRelative Frequency 60-690.3 70-790.35 80-890.275 90-990.025 100-1090.025 110-1190 120-1290.025 Change into a relative frequency

23. Pulse RateFreq 60-6912 70-7914 80-8911 90-991 100-1091 110-1190 120-1291 Change into cumulative frequency

24. Pulse RateCumulative Freq 60-6912 70-7912+14 80-8912+14+11 90-9912+14+11+1 100-10912+14+11+1+1 110-11912+14+11+1+1+0 120-12912+14+11+1+1+0+1 Change into cumulative frequency

25. Pulse RateCumulative Freq 69 or less12 79 or less12+14=26 89 or less12+14+11=37 99 or less12+14+11+1=38 109 or less12+14+11+1+1=39 119 or less12+14+11+1+1+0=39 129 or less12+14+11+1+1+0+1=40 Change into cumulative frequency

26. Pulse RateCumulative Freq 69 or less12 79 or less26 89 or less37 99 or less38 109 or less39 119 or less39 129 or less40

27. Frequency Distributions Last Digit of female pulsesFrequency 09 10 28 30 46 50 67 70 810 90

28. Frequency Distributions IQFrequency 50-6924 70-89228 90-109490 110-129232 130-14926 IQ Scores from 1000 adults were randomly selected. The results are summarized below. Notice the frequencies start low, increase then decrease.

29. Histograms A histogram is a graph consisting of bars of equal width drawn adjacent to each other (without gaps). The Horizontal scale represents classes of quantitative data value and the vertical scale represents frequencies. The heights of the bars correspond to the frequency values.

30. Relative Frequency Histogram A relative frequency histogram is the same as a histogram with relative frequencies instead of frequencies.

31. Cumulative Histogram

32. This data because of its shape is said to have a normal distribution.

33. Histograms

35. Statistical Graphs obama-needs-charts-and-graphs

40. Homework 2-2: 1 -4, 5-17 odd. 2-3: 1-4, 5-19 odd. Read 2-4