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.

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

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.

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.

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

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.