unit 1.3 – descriptive statistics describing datasocsskewsymmetric time plotsseasonaltrendsbox and...

Unit 1.3 – Descriptive StatisticsDescribing Data SOCS Skew Symmetric

Time Plots Seasonal Trends Box and Whisker Variation 5-Number Summary

O-gives Relative Frequency Cumulative Relative CumulativeFrequency Frequency

Density Curves Normal Distribution Percentiles Z-scores

Unit 1.3 – Descriptive Statistics

Part 1Describing Data

SOCS

Skew

Symmetric

Unit 1.3 – Descriptive Statistics

Describing Data – SOCSShape – See the next slide

Outliers – Identify the outliers

Center – Mean and Median

Spread – Standard Deviation

70.2 77.4 74.7 90.9 104.481.9 85.5 86.4 86.4 75.674.7 68.4 94.5 84.6 81.9

Unit 1.3 – Descriptive StatisticsShape

Skew Left Skew Right SymmetricTypically due to an outlier Typically due to an outlier Can be folded at the medianon the left. Tail is on the left. on the right. Tail is on the right. to produce side to side symmetry

70.2 77.4 74.7 90.9 104.481.9 85.5 86.4 86.4 75.674.7 68.4 94.5 84.6 81.9

Unit 1.3 – Descriptive StatisticsMore on Symmetry…

Examples of perfect symmetry: Fairly Symmetric: Not very symmetric:

70.2 77.4 74.7 90.9 104.481.9 85.5 86.4 86.4 75.674.7 68.4 94.5 84.6 81.9

Unit 1.3 – Descriptive Statistics

Describing Data – SOCSShape – 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.

70.2 77.4 74.7 90.9 104.481.9 85.5 86.4 86.4 75.674.7 68.4 94.5 84.6 81.9

Unit 1.3 – Descriptive Statistics

Part 1 continued…Time Plots

Trends

Seasonal Variation

Unit 1.3 – Descriptive StatisticsTime Plots with Trends

Unit 1.3 – Descriptive StatisticsTime Plots with Seasonal Variation

Note that some also have trend

Unit 1.3 – Descriptive StatisticsPart 2

Relative Frequency

Cumulative Frequency

Relative Cumulative Frequency

Ogives

Percentiles

Unit 1.3 – Descriptive StatisticsAges of US Presidents

Frequency Relative Frequency

To calculate Relative Frequency, simply divide each Frequency value by the number of individuals (43).

Class Frequency40-44 245-49 650-54 1355-59 1260-64 765-69 3

Class Frequency Relative Frequency

40-44 245-49 650-54 1355-59 1260-64 765-69 3

2 / 43 = 4.651%

Unit 1.3 – Descriptive StatisticsCumulative Frequency

To calculate Cumulative Frequency for any particular row, sum the Frequency cells for that row and all previous rows.

Class Freq. Rel. Freq.40-44

2 4.651%

45-49

6 13.953%

50-54

13 30.233%

55-59

12 27.907$

60-64

7 16.279%

65-69

3 6.977%

Class Freq. Rel. Freq. Cumulative Frequency

40-44

2 4.651%

45-49

6 13.953%

50-54

13 30.233%

55-59

12 27.907$

60-64

7 16.279%

65-69

3 6.977%

40

Unit 1.3 – Descriptive StatisticsRelative Cumulative

Frequency

To calculate the Relative Cumulative Frequency, simply divide the corresponding Cumulative Frequency by the number of individuals.

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. CumulativeFrequency

RelativeCumulativ

e Frequency

40-44 2 4.651% 245-49 6 13.953% 850-54 13 30.233% 2155-59 12 27.907$ 3360-64 7 16.279% 4065-69 3 6.977% 43

40 / 43 = 93.023%

Unit 1.3 – Descriptive StatisticsComplete Frequency Table

Class Freq. Rel. Freq. CumulativeFrequency

RelativeCumulativ

e 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 StatisticsComplete Frequency Table to O-give

Class Freq. Rel. Freq. CumulativeFrequency

RelativeCumulativ

e 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 StatisticsComplete Frequency Table to O-give

Class Freq. Rel. Freq. CumulativeFrequency

RelativeCumulativ

e 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 StatisticsInterpreting an O-give

What percentile was Bill Clinton in for age of Presidents at inauguration?

Unit 1.3 – Descriptive StatisticsInterpreting an O-give

What percentile was Bill Clinton in for age of Presidents at inauguration?

Unit 1.3 – Descriptive StatisticsInterpreting an O-give

Which percent of presidents were younger than 58 years old at inauguration?

Unit 1.3 – Descriptive StatisticsInterpreting 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?