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Descriptive Statistics

Descriptive Statistics. Graphical Descriptive Measures Numerical Descriptive Measures. Central Tendency: the center of the distribution Variability: how measurements vary about the center of the distribution. Population: parameters Sample: statistics. Mode.

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Descriptive Statistics

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  1. Descriptive Statistics • Graphical Descriptive Measures • Numerical Descriptive Measures

  2. Central Tendency: the center of the distribution • Variability: how measurements vary about the center of the distribution

  3. Population: parameters • Sample: statistics

  4. Mode • Measurement within a set that occurs most often (for grouped data = midpoint of interval) • Can be more than one • Not influenced by extreme measurements • Modes of subsets cannot be combined • For grouped data, values can change depending on categories used • Qualitative and quantitative- all levels of measurement

  5. Use of Mode • Measure of popularity • Qualitative data • Distributions that may be bimodal or trimodal

  6. Median • Middle value when measurements are arranged in order of magnitude (50% above;50% below) • only one • not influenced by extreme measurements • cannot be combined • stable value even if grouped data are reorganized into different categories • quantitative data only-any scale except nominal

  7. 11 22 32 42 51 66 776 11 12 13 14 15 16 ] • Visual Method: • Order values. • Count to value that results in equal numbers above and below. • (N+1)/2 • Use average for even data sets. Take value that separates two groups for odd data sets

  8. Median from Grouped Data • Actual value is not known • (N+1)/2 to find # of frequencies above or below ‘i;’ which contains median • (100+1)/2=50.5 • Median is in interval 51-53 …52

  9. Median of grouped data

  10. Class IntervalFrequency 0.5-2.5 4 2.5-4.5 2 4.5-6.5 4 6.5-8.5 5 8.5-10.5 3 • 10 2 1 • 5 7 • 7 10 • 4 3 • 6 8 • 2 8 • [18+1]/2=19/2=9.5 • Midpoint=4.5-6.5=5.5

  11. Mean • Arithmetic average of the measurements in the data set • Only one • Influenced by extreme measurements • Means of subsets can be combined • Quantitative-requires ratio or interval data

  12. Population mean = m (parameter) • Sample mean = M (statistic) • For ungrouped data : M = Sxi/n • Where n = number of measurements; • xi = individual measurements • For grouped data: M = S fixi/n • Where: • f = frequency associated with class interval • x = midpoint of class interval

  13. Frequency distribution

  14. Grouped Data

  15. Class IntervalFrequencyMidpoint 0.5-2.5 4 2.5-4.5 2 4.5-6.5 4 6.5-8.5 5 8.5-10.5 3 • 10 2 1 • 5 7 • 7 10 • 4 3 • 6 8 • 9 2 8

  16. Mean of a set of means • You can combine means if the N’s of the samples are equal • If the N’s are not equal they can be combined, but carefully

  17. 3.41 3.63 3.37 2.16 3.80 16.37 16.3/5=3.27 Flawed Method For Calculating Semester GPA Mean of a set of means

  18. Correct method

  19. Finally • M=282/87=3.24

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