unit 1.3 – descriptive statistics describing datasocsskewsymmetric time plotsseasonaltrendsbox and...
DESCRIPTION
Unit 1.3 – Descriptive Statistics Describing Data – SOCS Shape – See the next slide Outliers – Identify the outliers Center – Mean and Median Spread – Standard DeviationTRANSCRIPT
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?
