Chapter 3 Measuring Central tendency and Variability.pptx

Primary data

• Specific information collected by the person who is doing the research.

Secondary data


• Any material that has been collected from published records

1. DATA COLLECTION & DATA PRESENTATION 1

2. Sources of Data 2 Primary data • Specific information collected by the person who is doing the research. Secondary data • Any material that has been collected from published records

3. Data Collection Methods How to reach respondents in order to obtain the required data? 1.Observation 2. Experimentation 3. Interviewing 4. Mail Survey 5. Questionnaires 3

4. Data Presentation Frequency table • Bar chart • Pie chart • Histogram Pictogram 4

5. Mean, Median, Mode, and Range

6. Today we will be learning about Statistics . Statistics is a branch of mathematics that deals with collecting and analyzing a set of data. When data has been collected, statisticians like to “measure” two things: 1) Center 2) Variability Introduction

7. Section 1: Measures of Center

8. A measure of center is one number that represents the center of a set of data. There are three different ways you can find the center: Mean Median Mode Measures of Center

9. Mean Mean = Average

10. What is the Mean? The Mean is the average. Two simple steps will give you the mean of a set of numbers . Mean = Average Your report card has an average on it. Step 1 Add the numbers. Step 2 Divide by the # of items in the dataset.

11. DATASET: 2 , 3 , 1 , 1 , , 1 , 2 , 4 Add the numbers: 2 + 3 + 1 + 1 + + 1 + 2 + 4 = Divide by total items: 14 ÷ 8 = Mean Step 1 Add the numbers. Step 2 Divide by the # of items in the dataset. 14 Example of Mean: 1.75

12. Median Median = Middle

13. What is the Median? The Median is the middle number. How do you find the Median? Median = Middle ORDER the numbers. If there is just 1 middle #: your done! If there are 2 middle #’s FIND the middle #. Average the 2 middle numbers.

14. ORDER the numbers. If there is just 1 middle #: your done! If there are 2 middle #’s FIND the middle #. Average the 2 middle numbers. Add the 2 middle numbers Then, Divide by 2 Example of Median DATASET: 2 , 3 , 1 , 1 , , 1 , 2 , 4 Arrange in order: 1 + 2 = 3 3 ÷ 2 = Median 1.5

15. Mode Mo de = Mo st

16. The Mode is the number (or item) that appears the Most often. You can have 1 mode. You can have more than 1 mode. There may be no mode at all! Mo de = Mo st What is Mode?

17. Example of Mode You can determine Mode with numerical or non-numerical data. Which beverage appears most often? Cokes That’s your mode!

18. Example of Mode DATASET: 2 , 3 , 1 , 1 , , 1 , 2 , 4 Mode 1

19. Section 2: Measures of Variability

20. A measure of variability (or variation) is used to describe how spread out the data is. Range Mean Deviation Deviation Variance Standard Deviation   Measures of Variability

21. Range Range = Biggest – Smallest

22. What is the Range? The Range is the difference between the biggest number and the smallest number. Range = Biggest Smallest  

23. Example of Range Range = B iggest – Smallest DATASET: 2 , 3 , 1 , 1 , , 1 , 2 , 4 Subtract: 4 – 0 = Range 4

24. You Try #1 Ahmed’s math test scores: 90 , 85 , 80 , 70 , 90 , 65 Mean _____ Median _____ Mode _____ Range _____

25. You Try #3 Which data set has the greatest Range 7,10,2, 6, 12 13,9, 9, 10, 11 20, 20, 18, 15, 15

26. Mean deviation/Deviation 26 How far, on average, all values are from the middle. For  deviation  just think  distance In three steps: Find the  mean  of all values 2. Find the  distance  of each value from that mean (subtract the mean from each value, ignore minus signs) 3. Then find the  mean of those distances

27. Example: find the Mean Deviation of 3, 6, 6, 7, 8, 11, 15, 16 27 Step 1 : Find the  mean : Mean =   =     = 9 Step 2: Find the  distance  of each value from that mean: Step 3. Find the  mean of those distances : Mean Deviation  =   3.75   Value Distance from 9 3 6 6 3 6 3 7 2 8 1 11 2 15 6 16 7 So, the  mean = 9 and the  mean deviation = 3.75 Subtracting 3-9 6-9 6-9 8-9 11-9 15-9 16-9

28. Example 2 :  Determine the mean deviation for the data values 5, 3,7, 8, 4, 9 28 Step 1 : Find the  mean : Mean =   = = 6 Step 2: Find the  distance  of each value from that mean: Step 3. Find the  mean of those distances : Mean Deviation   =   = = 2   Value Distance from 6 5 1 3 3 7 1 8 2 4 2 9 3 So, the  mean = 6 and the  mean deviation = 2 Subtracting 5-6 3-6 7-6 8-6 4-6 9-6

29. Summary.... Mean = Median = Mode = Range = Middle Average Most Biggest – Smallest

30. Remember.... Mean measures Center Median measures Center Range measures Variability

31. Variance and standard deviation 31 Standard Deviation : Put simply, standard deviation measures how far apart numbers are in a data set . Its symbol is  σ  (the greek letter sigma) The formula is easy: it is the  square root  of the  Variance.   Variance : variance measures how far each number in the set is from the mean (average), and thus from every other number in the set. To calculate the variance follow these steps: Find out the mean Then for each number subtract the mean and square the result. Then find out the average of those square differences.

32. Example 1 – Calculate the variance and standard deviation 32 Dataset : 25, 26, 27,30,32. First, we must find the mean Mean =   = = 28 2. Calculate the difference and square it Calculate the difference and square it 3. Calculate the variance : Variance =   = = 6.8 Sta ndard deviation = 2.607     Dataset Difference from 28 Squared result 25 25 – 28 = -3 (-3) 2 9 26 26 – 28 = -2 (-2) 2 4 27 27 – 28 = -1 (-1) 2 1 30 30 – 28 = 2 2 2 4 32 32 – 28 = 4 4 2 16

33. Example 2 – Calculate the variance and standard deviation 33 Dataset : 92, 95, 85, 80, 75, 50 First, we must find the mean Mean =   = = 79.5 2. Calculate the difference and square it 3. Calculate the variance : Variance =   = = 219.58 Sta ndard deviation = 14.818     Data set Difference from 79.5 Squared Result 92 92 – 79.5 =12.5 156.25 95 95 – 79.5 =15.5 240.25 85 85 – 79.5 = 5.5 30.25 80 80 – 79.5 =0.5 0.25 75 75 – 79.5 = -4.5 20.25 50 50 – 79.5 = -29.5 870.25

34. End of PowerPoint