1 / 20

Descriptive Statistics

This comprehensive guide delves into descriptive statistics, focusing on key measures of central tendency: mode, median, and mean. It explains how to determine each measure and discusses their influence on data analysis. The mode is prominent in qualitative data, while the median serves as a stable central value, minimally affected by outliers. The mean, representing the arithmetic average, may vary with extreme values. Additionally, the guide covers the methodologies for grouped and ungrouped data, providing valuable insights for effective data interpretation and evaluation.

rashad
Télécharger la présentation

Descriptive Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related