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DESCRIPTIVE DATA ANALYSIS: MEAN, MEDIAN AND MODE

DESCRIPTIVE DATA ANALYSIS: MEAN, MEDIAN AND MODE. Dr. Muhammad Tanveer Afzal LECTURER SECONDARY TEACHER EDUCATION. Statistics. A set of mathematical procedures for describing , synthesizing , analyzing, and interpreting quantitative data.

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DESCRIPTIVE DATA ANALYSIS: MEAN, MEDIAN AND MODE

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  1. DESCRIPTIVE DATA ANALYSIS: MEAN, MEDIAN AND MODE Dr. Muhammad Tanveer Afzal LECTURER SECONDARY TEACHER EDUCATION

  2. Statistics... • A set of mathematical procedures for describing, synthesizing, analyzing, and interpreting quantitative data …the selection of an appropriate statistical technique is determined by the research design, hypothesis, and the data collected

  3. Preparing data for analysis... Data must be accurately scored and systematically organized to facilitate data analysis: scoring: assigning a total to each participant’s instrument tabulating: organizing the data in a systematic manner coding: assigning numerals (e.g., ID) to data

  4. Descriptive Statistics Gives numerical and graphic procedures to summarize a collection of data in a clear and understandable way Inferential Statistics Provides procedures to draw inferences about a population from a sample Statistics

  5. Definitions • Data: Information (usually in statistics we use numerical information) • Note: the word data is plural! • One piece of data is called a datum.

  6. Measurement “If a thing exists, it exists in some amount; and if it exists in some amount, it can be measured.” –E. L. Thorndike (1914)

  7. Measurement “If you haven't measured it you don't know what you are talking about.” -Lord Kelvin

  8. Definitions • Inference: To draw a conclusion (Example: when you see smoke, you infer that there’s a fire) • Population: The entire group of interest (Example: Every mongoose on the island of Hawaii) • Sample: A subset of the population (Example: A group of 100 mongooses that I’m studying in Pahoa)

  9. Nominal Scales Four Basic Scales of Measurement Ordinal Scales Interval Scales Ratio Scales

  10. Types of Measurement Scales • Nominal • scores only reflect the property of difference so the "numbers" have no numerical meaning. • Sometimes called categorical, discontinuous, or qualitative variables. • Mode is only appropriate measure of central tendency • E.g., biological sex, race, breed, etc… • Ordinal • scores do indicate the property of magnitude, but do not reflect equal intervals. • the median is the appropriate measure of central tendency on ordinal scales • e.g., "class rank”

  11. Types of Measurement Scales • Interval • possess both properties of difference and magnitude, but also have the property of equal intervals. • e.g., intelligence or other test scores. • Ratio • possess all of the properties of difference, magnitude, equal intervals, and an absolute, or true zero (a "0" means the complete absence of the thing being measured) • e.g., weight, height, distance, reaction time

  12. Descriptive Measures • Central Tendency measures. They are computed to give a “center” around which the measurements in the data are distributed. • Variation or Variability measures. They describe “data spread” or how far away the measurements are from the center. • Relative Standing measures. They describe the relative position of specific measurements in the data.

  13. “Central Dogma” of Statistics

  14. Descriptive statistics? Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics provides simple summaries about the sample and about the observations that have been made.

  15. Measurement of Central Tendency Mean Median Mode

  16. Measures of Central Tendency • Mean: Sum of all measurements divided by the number of measurements. • Median: A number such that at most half of the measurements are below it and at most half of the measurements are above it. • Mode: The most frequent measurement in the data.

  17. Mean The Mean or average is probably the most commonly used method of describing central tendency. To compute the mean all you do is add up all the values and divide by the number of values. For Example 15, 20, 21, 20, 36, 15, 25, 15 The sum of these 8 values is 167, so the mean is 167/8 = 20.875.

  18. MEAN = 40/10 = 4 Notice that the sum of the “deviations” is 0. Notice that every single observation intervenes in the computation of the mean. Example of Mean

  19. Central Tendency – “Mean”, • For individual observations, . E.g. X = {3,5,7,7,8,8,8,9,9,10,10,12} = 96 ; n = 12 • Thus, = = 96/12 = 8 • The above observations can be organized into a frequency table and mean calculated on the basis of frequencies Thus, = 96/12 = 8

  20. Central Tendency–“Mean of Grouped Data” • House rental or prices in the PMR are frequently tabulated as a range of values. E.g. • What is the mean rental across the areas? = 23; = 3317.5 Thus, = 3317.5/23 = 144.24

  21. Median The Median is the score found at the exact middle of the set of values. One way to compute the median is to list all scores in numerical order, and then locate the score in the center of the sample. Example: For example, if there are 500 scores in the list, score #250 would be the median. If we order the 8 scores shown above, we would get: 15,15,15,20,20,21,25,36 There are 8 scores and score #4 and #5 represent the halfway point. Since both of these scores are 20, the median is 20. If the two middle scores had different values, you would have to interpolate to determine the median.

  22. Median: (4+5)/2 = 4.5 Notice that only the two central values are used in the computation. The median is not sensible to extreme values Example of Median

  23. Mode Mode is the value occurring most often in the data. If the largest group of people in a sample measuring age were 25 years old, then 25 would be the mode. The mode is the least commonly used measure of central tendency, particularly in large data sets. However, the mode is still important for describing a data set, especially when more than one value occurs frequently.

  24. Mode Problem: The number of points scored in a series of football games is listed below. Which score occurred most often?   7,  13,  18,  24,  9,  3,  18 Solution: Ordering the scores from least to greatest, we get:   3,  7,  9,  13,  18,  18,  24 Answer:   The score which occurs most often is 18. This problem really asked us to find the mode of a set of 7 numbers. Definition:   The mode of a set of data is the value in the set that occurs most often.

  25. In this case the data have tow modes: 5 and 7 Both measurements are repeated twice Example of Mode

  26. Mode: 3 Notice that it is possible for a data not to have any mode. Example of Mode

  27. “Central Tendency”

  28. 0.1% The Empirical Rule 99.7% of data are within 3 standard deviations of the mean 95% within 2 standard deviations 68% within 1 standard deviation 34% 34% 2.4% 2.4% 0.1% 13.5% 13.5% x - 3s x - 2s x - s x x+s x+2s x+3s

  29. ?Thanks for your patience

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