1. Analyzing Frequency Distributions

2. 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

3. A second grade teacher gave her students a word recognition test
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}

4. Score
Frequency
Cum freq.
Percent freq
Cum. Per. Dist.

5. 10 11 12 13 15 16 17 18 20 22 24 Score Frequency Cum freq.
Percent freq
Cum. Per. Dist. 10 11 12 13 15 16 17 18 20 22 24

6. 10 2 11 12 3 13 15 1 16 17 4 18 20 22 24 Score Frequency Cum freq.
Percent freq
Cum. Per. Dist. 10 2 11 12 3 13 15 1 16 17 4 18 20 22 24

7. Score
Frequency
Cum freq.
Percent freq
Cum. Per. Dist. 10 2 11 4 12 3 7 13 15 1 16 17 18 20 22 24 25

8. Score
Frequency
Cum freq.
Percent freq
Cum. Per. Dist. 10 2 8% 11 4 12 3 7
12% 13 15 1 4% 16 17
16% 18 20 22 24 25

9. Score
Frequency
Cum freq.
Percent freq
Cum. Per. Dist. 10 2 8% 8 11 4 16 12 3 7
12% 28 13 40 15 1 4% 44 48 17
16% 64 18 72 20 80 22 88 24 25
100

10. 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}

11. Score
Frequency
Cumulative frequency
Percentage frequency
Cum. Per. Dist.

12. Score
Frequency
Cumulative frequency
Percentage frequency
Cum. Per. Dist. 10 2 11 4 12 14 15 3 16 17 1 18 19 20

13. Score
Frequency
Cumulative frequency
Percentage frequency
Cum. Per. Dist. 10 2 11 4 6 12 8 14 15 3 13 16 17 1 18 19 20

14. Score
Frequency
Cumulative frequency
Percentage frequency
Cum. Per. Dist. 10 2 11 4 6 20 30 12 8 40 14 50 15 3 13 65 16 80 17 1 5 85 18 90 19 95
100

15. Categorical frequency table
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

16. 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