Unit 1.3 – Descriptive Statistics
Describing Data
SOCS
Skew
Symmetric
Time Plots
Seasonal
Variation
Trends
Box and Whisker
5-Number Summary
O-gives
Relative Frequency
Cumulative
Frequency
Relative Cumulative
Frequency
Density Curves
Normal Distribution
Percentiles
Z-scores
Unit 1.3 – Descriptive Statistics
Part 1
Describing Data
SOCS
Skew
Symmetric
Unit 1.3 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Describing Data – SOCS
Shape – See the next slide
Outliers – Identify the outliers
Center – Mean and Median
Spread – Standard Deviation
Unit 1.3 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Shape
Skew Left
Skew Right
Symmetric
Typically due to an outlier
Typically due to an outlier
Can be folded at the median
on the left. Tail is on the left.
on the right. Tail is on the right.
to produce side to side symmetry
Unit 1.3 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
More on Symmetry…
Examples of perfect symmetry: Fairly Symmetric:
Not very symmetric:
Unit 1.3 – Descriptive Statistics
70.2
77.4
74.7
90.9
104.4
81.9
85.5
86.4
86.4
75.6
74.7
68.4
94.5
84.6
81.9
Describing Data – SOCS
Shape – This distribution would be fairly
symmetric but the outlier is skewing it right.
Outliers – 104.4 is an outlier to the right.
Center – Mean and Median
The mean (82.5) is higher than the median (81.9).
Spread – Standard Deviation
The standard dev is 9.577 and the range is 36.
Unit 1.3 – Descriptive Statistics
Part 1 continued…
Time Plots
Trends
Seasonal Variation
Unit 1.3 – Descriptive Statistics
Time Plots with Trends
Unit 1.3 – Descriptive Statistics
Time Plots with Seasonal Variation
Note that some also have trend
Unit 1.3 – Descriptive Statistics
Part 2
Relative Frequency
Cumulative Frequency
Relative Cumulative Frequency
Ogives
Percentiles
Unit 1.3 – Descriptive Statistics
Ages of US Presidents
Frequency
Relative Frequency
Class
Frequency
Class
Frequency
40-44
2
40-44
2
45-49
6
45-49
6
50-54
13
50-54
13
55-59
12
55-59
12
60-64
7
60-64
7
65-69
3
65-69
3
Relative Frequency
2 / 43 = 4.651%
To calculate Relative Frequency, simply divide each
Frequency value by the number of individuals (43).
Unit 1.3 – Descriptive Statistics
Cumulative Frequency
Class
Freq.
Rel. Freq.
40-44
2
4.651%
45-49
6
50-54
Class
Freq.
Rel. Freq.
13.953%
40-44
2
4.651%
13
30.233%
45-49
6
13.953%
55-59
12
27.907$
50-54
13
30.233%
60-64
7
16.279%
55-59
12
27.907$
65-69
3
6.977%
60-64
7
16.279%
65-69
3
6.977%
Cumulative
Frequency
40
To calculate Cumulative Frequency for any particular row,
sum the Frequency cells for that row and all previous
rows.
Unit 1.3 – Descriptive Statistics
Relative Cumulative Frequency
Class
Freq.
Rel. Freq.
Cumulative
Frequency
40-44
2
4.651%
2
45-49
6
13.953%
8
50-54
13
30.233%
21
55-59
12
27.907$
33
60-64
7
16.279%
40
65-69
3
6.977%
43
Class
Freq.
Rel. Freq.
Cumulative
Frequency
40-44
2
4.651%
2
45-49
6
13.953%
8
50-54
13
30.233%
21
55-59
12
27.907$
33
60-64
7
16.279%
40
65-69
3
6.977%
43
Relative
Cumulative
Frequency
40 / 43 = 93.023%
To calculate the Relative Cumulative Frequency, simply divide the
corresponding Cumulative Frequency by the number of individuals.
Unit 1.3 – Descriptive Statistics
Complete Frequency Table
Class
Freq.
Rel. Freq.
Cumulative
Frequency
Relative
Cumulative
Frequency
40-44
2
4.651%
2
4.651%
45-49
6
13.953%
8
18.605%
50-54
13
30.233%
21
48.837%
55-59
12
27.907$
33
76.744%
60-64
7
16.279%
40
93.023%
65-69
3
6.977%
43
100%
Unit 1.3 – Descriptive Statistics
Complete Frequency Table to O-give
Class
Freq.
Rel. Freq.
Cumulative
Frequency
Relative
Cumulative
Frequency
40-44
2
4.651%
2
4.651%
45-49
6
13.953%
8
18.605%
50-54
13
30.233%
21
48.837%
55-59
12
27.907$
33
76.744%
60-64
7
16.279%
40
93.023%
65-69
3
6.977%
43
100%
Unit 1.3 – Descriptive Statistics
Complete Frequency Table to O-give
Class
Freq.
Rel. Freq.
Cumulative
Frequency
Relative
Cumulative
Frequency
40-44
2
4.651%
2
4.651%
45-49
6
13.953%
8
18.605%
50-54
13
30.233%
21
48.837%
55-59
12
27.907$
33
76.744%
60-64
7
16.279%
40
93.023%
65-69
3
6.977%
43
100%
Unit 1.3 – Descriptive Statistics
Interpreting an O-give
What percentile was Bill Clinton in for age of Presidents
at inauguration?
Unit 1.3 – Descriptive Statistics
Interpreting an O-give
What percentile was Bill Clinton in for age of Presidents
at inauguration?
Unit 1.3 – Descriptive Statistics
Interpreting an O-give
Which percent of presidents were younger than 58 years
old at inauguration?
Unit 1.3 – Descriptive Statistics
Interpreting an O-give
If a presidential candidate is said to be in the 80th
percentile for Age for all former presidents, how old are
they?