Graphing Data

Graphing Data Frequency

Distributions DV Freq.1 22 43 104 255 366 187 78 29 1

05

10152025303540

Freq

uenc

y

1 2 3 4 5 6 7 8 9DV

Graphing Data Frequency Distributions

Each value of interest listed on the x-axis Best suited when variable has small,

finite number of possible values

What types of variables fit this definition?

Graphing Data Stem-and-Leaf Displays

Raw Data Stem Leaf0 1 1 2 2 3 4 4 4 5 5 5 6 6 7 7 7 7 8 8 9 0 0112234445556677778899

10 11 11 11 12 12 12 13 13 13 13 13 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 17 17 17 18 18 18 18 19 19

1 0111222333334445555556666666666777888899

20 20 21 21 22 22 23 23 24 24 24 24 25 25 26 26 27 28 28 29 2 00112233444455667889

30 30 35 3 005

Graphing Data Stem and leaf displays

“Stem” = “Leading Digit” = “Most Significant Digit”

“Leaf” = “Trailing Digit” = “Least Significant Digit”

Unlike frequency distribution, can reconstruct entire raw data set very easily

Stem is typically tens digit (Xx), but can be hundreds (Xxx) if all values are 100+ or the thousands (Xxxx) if all values are 1,000+

Bad if we have many of our values under one stem

Graphing Data Stem-and-Leaf Displays

0

50

100

150

200

250Fr

eque

ncy

1 2 3 4 5 6 7 8 9DV

Graphing Data Stem-and-Leaf Displays

BDI2TOT Stem-and-Leaf Plot Frequency Stem & Leaf

28.00 0 * 000000000000000011111111111125.00 0 t 222222222222333333333333323.00 0 f 4444444444445555555555530.00 0 s 66666666666666666677777777777722.00 0 . 888888888889999999999917.00 1 * 0000000111111111118.00 1 t 22222222222333333314.00 1 f 444444445555559.00 1 s 66666777718.00 1 . 8888888899999999996.00 2 * 0001112.00 2 t 336.00 2 f 4455554.00 2 s 66772.00 2 . 881.00 3 * 12.00 3 t 2211.00 Extremes (>=35)Stem width: 10Each leaf: 1 case

Graphing Data Put the following data in a stem and leaf

plot using the *, t, f, s, . system0 1 1 2 2 3 4 4 4 5 5 5 6 6 7 7 7 7 8 8 910 11 11 11 12 12 12 13 13 13 13 13 14 14 14 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 17 17 17 18 18 18 18 19 1920 20 21 21 22 22 23 23 24 24 24 24 25 25 26 26 27 28 28 2930 30 35

Graphing Data

BDI2TOT

100.090.080.070.060.050.040.030.020.010.00.0

Frequency

120

100

80

60

40

20

0

Histograms Bars represent certain interval – in this case 10 units

1st bar = 0-10, 2nd bar = 11-20, etc. Best for data that fall into intervals naturally, i.e. discrete,

categorical, nominal or sometimes ordinal variables

Graphing Data

BDI2TOT

100.090.080.070.060.050.040.030.020.010.00.0

Frequency

120

100

80

60

40

20

0

Histograms When choosing graph intervals, only rule is to

maximize quick readability Outlier

Graphing Data Histograms

2nd bar = 11-20 In practice though, a score of 10.5 would be

rounded to 11, and a score of 20.4 to 20, and so our actual range is from 10.5 – 20.4 these are called the real upper limits and the

real lower limits 11-20 = upper and lower limits 10.5-20.4 = real upper and lower limits

What are the real limits for our 3rd bar (21-30)?

Graphing Data

BDI2TOT

43

40

36

32

28

26

24

21

19

17

15

13

11

9

7

5

3

1

Missing

Frequency

20

10

0

Line Graphs Best for when data continuous, dimensional, or on

interval or ratio scales Same as previous histogram, but provides much

richer information if this information is meaningful, use a line graph – if

it’s just noise, use a bar graph

Graphing Data

Graphing Data

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6

Series3

Series2

Series1

Graphing Data Ways to Describe a Graph:

Symmetry

Modality

Skewness

Kurtosis

Graphing Data Ways to Described a Graph:

Symmetry (the graph below is Symmetric)

Graphing Data Ways to Described a Graph:

Modality (the graph below is Bimodal)

Graphing Data Ways to Described a Graph:

Skewness (the graph below is Right/Positively Skewed, and hence Non-symmetric)

Graphing Data Ways to Described a Graph:

Kurtosis

Graphing Data Ways to Described a Graph:

Kurtosis

Graphing Data Ways to Described a Graph:

Kurtosis