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# Problems 1 and 2 below refer to the following data for the variable &amp;quot;cognitive ability&amp;quot;: 100 90 80 100 90 110 130 100 120 80 110...

Attached please find the course exercises and a guide to using Excel to make a histogram.

Scores Bin
30 52.04 6.32 Bin Frequency
36 46.74 20.24 2
42 41.44 25.54 2
36 36.14 30.84 5
30 30.84 36.14 20
52 25.54 52 largest value 41.44 6
36 20.24 15 smallest value 46.74 3
34 52.04 2
36 5.29 class width More 0
33
30 46.75-52.04
32 41.45-46.74
35 36.15-41.44
32 30.85-36.14
37 25.55-30.84
34 20.25-25.54
36 14.95-20.24
31
35 52.04
20 46.74
24 41.44
46 36.14
23 30.84
31 25.54
32 20.24
45
34
37
28
40
34
38
40
52
31
33
15
27
36
40

References:

Aron, A., Aron, E., & Coups, E. J. (2009). Statistics for psychology (5th ed.). Upper Saddle River, NJ: Pearson Education.

Sturges, H. A. (1926). The choice of a class interval. Journal of the American Statistical Association, 21, 65-66.
Problems 1 and 2 below refer to the following data for the variable "cognitive ability": 100 90 80 100 90 110 130 100 120 80 110 80 130 120 130 130 100 110 110 100 100 100 120 130 80 Problem 1: Construct a frequency distribution (non-grouped) that summarizes the data for "cognitive ability": Cognitive Ability Frequency Total Problem 2: Construct a relative frequency distribution (non-grouped) for the "cognitive ability" data: Cognitive Ability Relative Frequency Total Problems 3, 4, and 5 below refer to the following data for the variable "cognitive ability": 102 107 104 125 125 105 98 101 118 100 100 115 102 119 108 98 110 114 128 100 110 109 121 128 102 103 97 111 100 117 103 105 106 106 107 108 107 107 106 119 110 111 109 108 111 111 109 110 108 110 Problem 3: Construct a grouped frequency distribution that summarizes the data for "cognitive ability": You can use the following formula to determine the number of classes: k = 1 + 3.3 log10 N (Sturges, 1926), where "k" = number of classes, "log10" = logarithm of base 10 of a number, and "N" = number of scores. For example, if our number of scores were 80, we would write the following formula in Excel: =1+3.32*(LOG10(80)), which would return a value of 7.318259, which rounded to a whole value (integer) would be 7. So, in this case we would use 7 classes. To figure the class size or "width", you can use the following formula: W = (largest value-smallest value)/k, where k = number of classes. would be 11. So, the intervals in this example would be as follows: 69-80; 81-92; 93-104; 105-116; 117-128; 129-140; and 141-152. Problem 4: Construct a grouped relative frequency distribution for the "cognitive ability" data: Problem 5: Using the grouped frequency distribution you made in problem 3, construct (a) a histogram, and (b) describe the shape of the distribution (i.e., symmetrical, approximately symmetrical, unimodal, multimodal, positively skewed, negatively skewed?) Reference: Week 2 Problems - Due Week 2, Day 7 (Monday) Post this assignment in the Assignment section as a Microsoft® Word or Microsoft® Excel attachment: Suppose that in our example above, our highest value were 150 and our lowest value were 70. So, W = 150-70/7 = 80/7 = 11.42 ≈ 11. In this case the class size Sturges, H. A. (1926). The choice of a class interval. Journal of the American Statistical Association, 21, 65-66.
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