frequency distribution scoresfrequencyrelative frequency cumulative frequency cumulative relative...
TRANSCRIPT
STATISTICSANDDATA
ANALYSISDAY 4
ESTIMATING MEANS AND MEDIANS FOR
FREQUENCY DISTRIBUTIONS
Frequency Distribution
Scores Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency
60-70 9 9
70-80 10 19
80-90 12
90-100 3
26.034
9
56.034
19
91.034
31
0.134
34
26.034
9
29.034
10
35.034
12
09.034
3
31
34
To find the approximate mean of the data from the frequency table. • First, identify the class marks (average of
upper and lower limit for each interval).• Put the class marks in L1 under STAT, EDIT.• Put the frequency of each interval under
L2 under STAT, EDIT.
• Next, go to STAT, CALC, 1-Var STATS, L1, L2, enter
Approximate Mean is 77.6The actual mean from original data was 77.8
Estimate the Mean for each frequency distribution.
Ages Frequency
10-20
20-30
30-40
40-50
50-60
4
75
2
2
Scores Frequency
1-3
3-5
5-7
7-9
9-11
1
1
58
9Height Frequency
60-65
65-70
70-75
75-80
80-85
6
6
4
11
Frequency DistributionScores Frequency Relative
FrequencyCumulative Frequency
Cumulative Relative
Frequency60-70 9 9
70-80 10 19
80-90 12
90-100 3
Scores Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency60-70 9 9
70-80 10 19
80-90 12
90-100 3
26.034
9
56.034
19
91.034
31
0.134
34
26.034
9
29.034
10
35.034
12
09.034
3
31
34
The median class is the class or interval that contains the median. • Since we know that the median is the middle point, with 50% of the data lying below it, then we just need to find
the class/interval where the 50th percentile would occur. • Using the cumulative relative frequencies we can easily see where the 50th percentile would lie.
Median Class is 70-80.
Estimating the median is done using a proportion, the median class (70-80) and the class just before the median class (60-70) and their cumulative relative frequencies, (.56 and .26 respectively). Remember, the median has a cumulative relative frequency of .5. 78Med
26.56.
26.5.
7080
70
Med
3.24.
10
70
Med
8.010
70
Med
870 Med
Med
ian
is b
etw
een
70 &
80
Ages Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency10-20
20-30
30-40
40-50
50-60
4
75
2
2
2.020
4
55.020
11
25.020
5
1.020
2
1.020
2
4
16
11
18
20 0.120
20
35.020
7
9.020
18
8.020
16
2.020
4
Find the Median Class and estimate the Median for each frequency distribution.
Median Class is 20-30.
6.28Med
2.55.
2.5.
2030
20
Med
35.30.
10
20
Med
8571428571.010
20
Med
571428571.820Med
Find the Median Class and estimate the Median for each frequency distribution.
Median Class is 7-9.
2.8Med
29.63.
29.5.
79
7
Med
34.21.
2
7
Med
6176470588.02
7
Med
235294118.17 Med
Scores Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency
1-3
3-5
5-7
7-9
9-11
1
15
8
9
04.024
1
04.024
1
21.024
5
33.024
8
38.024
9
1
27
15
24
04.024
1
08.024
2
29.024
7
63.024
15
0.124
24
Height Frequency Relative Frequency
Cumulative Frequency
Cumulative Relative
Frequency60-65
65-70
70-75
75-80
80-85
6
6
4
11
33.018
6
33.018
6
22.018
4
06.018
1
06.018
1
6
12
16
1817
33.018
6
67.018
12
89.018
16
94.018
17
0.118
18
Find the Median Class and estimate the Median for each frequency distribution.
Median Class is 65-70.
5.67Med
33.67.
33.5.
6570
65
Med
34.17.
5
65
Med
5.05
65
Med
5.265Med