STATISTICSANDDATA

ANALYSISPART 3

Created by: Tonya Jagoe

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 at or 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

438571428571.010

20

Med

295714285714.820Med

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