Transcript Analyzing Frequency Distributions

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:
{13,12,16,20,22,17,12,22,24,18,11,17,15,1
7,12,13,24,18,10,11,24,17,13,20,10}
Score
Frequency
Cum freq.
Percent freq
Cum. Per. Dist.
Score
10
11
12
13
15
16
17
18
20
22
24
Frequency
Cum freq.
Percent freq
Cum. Per. Dist.
Score
Frequency
10
11
12
13
15
16
17
18
20
22
24
2
2
3
3
1
1
4
2
2
2
3
Cum freq.
Percent freq
Cum. Per. Dist.
Score
Frequency
Cum freq.
10
11
12
13
15
16
17
18
20
22
24
2
2
3
3
1
1
4
2
2
2
3
2
4
7
10
11
12
16
18
20
22
25
Percent freq
Cum. Per. Dist.
Score
Frequency
Cum freq.
Percent freq
10
11
12
13
15
16
17
18
20
22
24
2
2
3
3
1
1
4
2
2
2
3
2
4
7
10
11
12
16
18
20
22
25
8%
8%
12%
12%
4%
4%
16%
8%
8%
8%
12%
Cum. Per. Dist.
Score
Frequency
Cum freq.
Percent freq
Cum. Per. Dist.
10
11
12
13
15
16
17
18
20
22
24
2
2
3
3
1
1
4
2
2
2
3
2
4
7
10
11
12
16
18
20
22
25
8%
8%
12%
12%
4%
4%
16%
8%
8%
8%
12%
8
16
28
40
44
48
64
72
80
88
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 =
{20,18,10,11,16,11,16,16,11,15,10,14,15,1
9,17,14,15,12,12,11}
Score
Frequency
Cumulative frequency
Percentage frequency
Cum. Per. Dist.
Score
Frequency
10
2
11
4
12
2
14
2
15
3
16
3
17
1
18
1
19
1
20
1
Cumulative frequency
Percentage frequency
Cum. Per. Dist.
Score
Frequency
Cumulative frequency
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
Percentage frequency
Cum. Per. Dist.
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
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
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