shapes of distributions

Shapes of Distributions

Frequency Distributions• Ex: X F

15 1

16 0

17 2

18 5

19 8

20 4

21 3

22 1

N= 24

Frequency Polygon

Frequency Polygon

• The greater the number of participants, the smoother the polygon shape- Curve

Normal CurveNormal Curve

Aka…Bell Curve, Bell-Shaped Curve, The CurveShape found often in natureUsed as the basis for a number of inferential statistics

Normal Distribution Examples

The Measures of Central Tendency and Distribution

When the mean, median, and mode are all at the same point, the center of the distribution, the data is considered to be normally distributed.

Mean, Median, Mode

The Measures of Central Tendency and Distribution

When data is skewed, values have “bunched” up at one end or the other.

With skewed data, the mean, median, and mode are usually all different values.

The distribution of the data can be positively or negatively skewed.

Positive Skew

Negative Skew

Bimodal

Distribution Shapes

Distribution Shapes

p. 19 Chapter 3 # 10

• Frequency Distribution and Percentages• Frequency Polygon based on Percentages• Number of Days Absent from Schools for a

sample of 10th graders• n = 28

Class Interval f %

6 – 13

13 – 20

20 – 27

27 – 34

34 – 41

41 – 48

48 – 55

55 – 62

62 – 69

69 – 76

76 – 83

83 – 90

90 – 97

97 – 104

104 – 111

111 - 118

Class Interval f %

6 – 13 2

13 – 20 3

20 – 27 8

27 – 34 4

34 – 41 3

41 – 48 1

48 – 55 2

55 – 62 1

62 – 69 1

69 – 76 0

76 – 83 1

83 – 90 0

90 – 97 1

97 – 104 0

104 – 111 0

111 - 118 1

Class Interval f %

6 – 13 2 7.1

13 – 20 3 10.7

20 – 27 8 28.6

27 – 34 4 14.3

34 – 41 3 10.7

41 – 48 1 3.6

48 – 55 2 7.1

55 – 62 1 3.6

62 – 69 1 3.6

69 – 76 0 0.0

76 – 83 1 3.6

83 – 90 0 0.0

90 – 97 1 3.6

97 – 104 0 0.0

104 – 111 0 0.0

111 - 118 1 3.6

0-613-20

27-3441-48

55-6269-76

83-90

97-104

111-1180

5

10

15

20

25

30

35

Attendance: Percentages

Attendance

Frequency Polygon w/ Percentages

0-6

118-

120

0-613-20

27-3441-48

55-6269-76

83-90

97-104

111-1180

1

2

3

4

5

6

7

8

9

Attendance: Frequencies

Attendance

0-6

118-

120