analyzing frequency distributions. five important characteristics of data distribution: the nature...
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Analyzing Frequency Distributions
Five important characteristics of data
• Distribution: the nature or shape of the distribution of the data, such as bell-shaped, uniform, or skewed
• Center: a representative value, such as an average, that indicates the middle
• Variation: a measure of the amount that the values vary among themselves; scattering
• Outliers: sample values that lie very far away from the vast majority of the other sample values
• Time: changing characteristics of the data over time
• A second grade teacher gave her students a word recognition test. The test consisted of 24 words. The kids’ scores are provided below. Use these scores to construct frequency, cumulative frequency, percentage frequency, and cumulative percentage distribution.
• Scores: {13,12,16,20,22,17,12,22,24,18,11,17,15,17,12,13,24,18,10,11,24,17,13,20,10}
Score Frequency Cum freq. Percent freq Cum. Per. Dist.
Score Frequency Cum freq. Percent freq Cum. Per. Dist.
10
11
12
13
15
16
17
18
20
22
24
Score Frequency Cum freq. Percent freq Cum. Per. Dist.
10 2
11 2
12 3
13 3
15 1
16 1
17 4
18 2
20 2
22 2
24 3
Score Frequency Cum freq. Percent freq Cum. Per. Dist.
10 2 2
11 2 4
12 3 7
13 3 10
15 1 11
16 1 12
17 4 16
18 2 18
20 2 20
22 2 22
24 3 25
Score Frequency Cum freq. Percent freq Cum. Per. Dist.
10 2 2 8%
11 2 4 8%
12 3 7 12%
13 3 10 12%
15 1 11 4%
16 1 12 4%
17 4 16 16%
18 2 18 8%
20 2 20 8%
22 2 22 8%
24 3 25 12%
Score Frequency Cum freq. Percent freq Cum. Per. Dist.
10 2 2 8% 8
11 2 4 8% 16
12 3 7 12% 28
13 3 10 12% 40
15 1 11 4% 44
16 1 12 4% 48
17 4 16 16% 64
18 2 18 8% 72
20 2 20 8% 80
22 2 22 8% 88
24 3 25 12% 100
• Students in a statistics class were given pretest at the beginning of the semester. The test consisted of twenty scores. Below you will find the scores obtained from twenty students in this class. Use these scores to construct frequency, cumulative frequency, percentage frequency, and cumulative percentage distribution and answer the questions listed below.
• Scores = {20,18,10,11,16,11,16,16,11,15,10,14,15,19,17,14,15,12,12,11}
Score Frequency Cumulative frequency Percentage frequency Cum. Per. Dist.
Score Frequency Cumulative frequency Percentage frequency Cum. Per. Dist.
10 2
11 4
12 2
14 2
15 3
16 3
17 1
18 1
19 1
20 1
Score Frequency Cumulative frequency Percentage frequency Cum. Per. Dist.
10 2 2
11 4 6
12 2 8
14 2 10
15 3 13
16 3 16
17 1 17
18 1 18
19 1 19
20 1 20
Score Frequency Cumulative frequency Percentage frequency Cum. Per. Dist.
10 2 2 10 10
11 4 6 20 30
12 2 8 10 40
14 2 10 10 50
15 3 13 15 65
16 3 16 15 80
17 1 17 5 85
18 1 18 5 90
19 1 19 5 95
20 1 20 5 100
• Lists categories or classes of scores, along with counts or frequencies of the number of scores that fall into each category.
• Lower class limits – the smallest numbers that can actually belong to the different classes
• Upper class limits – the largest numbers that can actually belong to different classes
• Class width (interval size)– difference between 2 consecutive lower class limits or boundaries
Categorical frequency table
How to find the size of the intervals:
• Decide on the number of classes your frequency table will contain, usually between 5 and 20
• Determine the class width by dividing the range by the number of classes, and round up, to guarantee all of the data will be in the table
• Select as the lower limit of the first class either the lowest score or a convenient value slightly less than the lowest score
• Add the class width until necessary intervals are achieved
• Make a frequency table with tally marks and record frequencies