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1. The following data set represents the amount spent (in dollars) by 45 shoppers at a supermarket. Construct a frequency distribution for the variable, and also report the relative frequencies for each class in your frequency distribution. NOTE: the data is in dollars and cents; you can not change that data! 1081, 1269, 1378, 15.23, 15.62. 17.00, 17.39. 18.36. 1843. 1927, 19.50.1954. 20.16, 20.59, 22.22, 23.04, 2447. 24.58, 25.13, 26.24.26.26, 27.65, 28.06, 28.08, 28.38, 32.03, 33.58, 34.98, 36.37, 37.44, 38.64. 39.16, 41.02, 42.97,44.08, 45.40, 48.65, 50.39, 52.75, 54.80, 59.07, 61.22. 62.32, 63.70, 66.76 2. A frequency Distribution is a universal descriptive tool. Briefly descripe what it is that we are trying to describe about the variable.

611078?module item id-12695791 notes for chapter 2, 2015.doc ne notes for chapter 2, 2015.doc (26 KB) Page of 2 -ZO Step 1. Put the data into an array. That is, list the observations from lowest to highest. This will give us some organization, and it will be very helpful in later steps. Step 2. Compute the range of the data. The range is the difference between the highest value and the lowest value in the data set. For this example the range is: 139- 68 71. We now know the total spread of our data, and we know that the frequency distribution must cover both of these valucs Step 3. Select the number of classes (groups) that you will use to summarize the data Students find this step confusing, but we will see that you already have some information o answer this question. A Rule of Thumb is that the number of classes should be at least 5 but not more than 15, and the less data you are working with the fewer the number っ b

3611078?module item id-12695791 notes for chapter 2, 2015.doc line notes for chapter 2, 2015.doc (26 KB) Page of classes that you will need to get a good summary. In our example, we have only 48 observations, so we should not need many classes to get a good summary. In step 2, we computed a range of 71. We need a distribution that will cover a range of at least 71 to get all of the values in. Step 4. Determine the class width. The class width is the interval between the lowest value in a class and the highest value in that class. Here we can put the steps together: If we try 5 classes, we would divide 71 by 5 14.2. We want a whole number as our class width, so we would round up to 15. If we try 6 classes: 71 /6-11.8, again we would round up to 12 or better, 15. Note that we desire a nice whole, round number for our class width to make the table easier to read. When you look back at the range of 71, you recognize that 8 classes of 10 units each should cover the range of 71 and give us a nice whole number as our width. Step 5. Select the class limits. The class limits are the low value and high value for each of our classes. The class limits can not overlap or they will confuse the reader. As long as the lowest value of your data can fit in the Is class and the highest value of your data can fit into the last class, the choice of class limits is an open question, but it makes sense to

1078?module item id-12695791 otes for chapter 2, 2015.doc e notes for chapter 2, 2015.doc (26 KB) Page 2 of 2 whole number as our width Step 5. Select the class limits. The class limits are the low value and high value for each of our classes. The class limits can not overlap or they will confuse the reader. As long as the lowest value of your data can fit in the I class and the highest value of your data can fit into the last class, the choice of class limits is an open question, but it makes sense to select class limits that are easy for the reader to recognize and understand. Keep in mind that various combinations of (1) the number of classes. (2) the width of the classes, and (3) the class limits will provide the reader with the same basic information about the variable. There is no one right answer. Try to make your distribution as easy as possible for the person using the information. Step 6. Set up the table of the distribution. Using our example of the number of questions answered correctly: Correct Answers 60 and under 70 70 and under 80 80 and under 90 90 and under 100 Relative Frequency 0.04 0.12 0.17 0.23 Frequency

s/73611078?module item id-12695791 ne notes for chapter 2, 2015.doc online notes for chapter 2, 2015.doc (26 KB) Page of 2 for the person using the information Step 6. Set up the table of the distribution. Using our example of the number of questions answered correctly Correct Answers 60 and under 70 70 and under 80 80 and under 90 90 and under 100 100 and under 110 110 and under 120 120 and under 130 130 and under 140 Frequency Relative Frequency 0.04 0.12 0.17 0.23 0.17 0.15 0.04 Total 48 1.00

1078?module item id-12695791 otes for chapter 2, 2015.doc e notes for chapter 2, 2015.doc (26 KB) 0.04 130 and under 140 Total 48 1.00 Step 7. One final step would be to graph the table as either a Histogram (vertical bar graph) or a Frequency Polygon (a line chart). A histogram is illustrated in the text. It lists the class limits on the horizontal scale and the frequencies (or relative frequencies) on the vertical scale, and raises a bar to the height of the frequency in each class.

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