central tendency
- 2. Summarizing Data And Measures Of Central Tendency Hina Fatima
- 3. Summarizing Data And Measures Of Central Tendency •What are statistics? •Why statistics? •Types of statistics
- 5. Statistics ? • Statistics is a branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation. https://en.wikipedia.org/wiki/Statistics
- 7. Add a Slide Title - 1
- 8. Importance of statistics Measurement and evaluation are essential part of teaching learning process. • It makes the teaching learning process more efficient. • You will become a better interpreter of educational data by mastering the statistical concepts.
- 9. Cont.… • It helps the teacher to predict the future performance of the pupils. • It enables the teacher to draw general conclusions. • You can Improve your teaching strategy. • It enables the teacher to summarize the results in a meaningful and convenient form.
- 12. Types Of Statistics • Descriptive statistics are simply numbers. For example percentages, numerals, fractions and decimals. • These numbers are used to describe or summarize a larger body numbers.
- 13. Tabulating Frequency Data • The frequency tabulation is a very popular method for summarizing data • In frequency distribution table, we organize the collected data into some classes or groups, and show the frequency in each group of scores. • The classroom teacher normally deals with a large amount of data usually in form of test scores. As the data increase it becomes more difficult to answer questions such as …..
- 14. Cont. …. • How many people are above average? • How many scored above the cut-off passing scores? • Did most of the class do well on the test? • What is the highest or lower score?
- 15. Frequency Distribution • Frequency is how often something occurs. • Suppose we obtain a set of numerical data like • 72, 75, 77, 67, 81, 68, 65, 86, 73, 67, 69, 82, 76, 76, 70, 83, 71, 63, 72, 72, 61, 84, 64, 67. • Step-I: Finding the Range: • Range of the series of any score can be found out by subtracting the lowest score from the highest. In the above set of scores, the range of the distribution is (86-61)=25.
- 16. Cont.… • Step-2: Determining the class interval • There are two different rules for determining the class interval. The First and easiest way is – the range is divided by the number of classes desired, e.g. • Where, i = class interval • Here, i = 25 / 5 = 5
- 17. Activity Time
- 18. Question • What is the range for the following set of numbers? 15, 21, 57, 43, 11, 39, 56, 83, 77, 11, 64, 91, 18, 37 Answer : 80 The range is the difference between the lowest and highest values. The highest value is 91. The lowest value is 11. Therefore the range = 91 - 11 = 80
- 19. Question • What is the range for the following set of numbers? 57, -5, 11, 39, 56, 82, -2, 11, 64, 18, 37, 15, 68 Answer = 87 The range is the difference between the lowest and highest values. The highest value is 82. The lowest value is -5. Therefore the range = 82 - (-5) = 82+5 = 87
- 20. Frequency Distribution • Example: siblings 2, 3, 1, 2, 1, 3, 2, 3, 4, 5, 4, 2, 2, 3
- 21. Example: Newspapers These are the numbers of newspapers sold at a local shop over the last 10 days: 22, 20, 18, 23, 20, 25, 22, 20, 18, 20 Let us count how many of each number there is: Papers Sold Frequency 18 2 19 0 20 4 21 0 22 2 23 1 24 0 25 1 It is also possible to group the values. Here they are grouped in: Papers Sold Frequency 15-19 2 20-24 7 25-29 1
- 22. Question Hockey team scored the following numbers of goals in their last twenty matches: 3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 3 • Which number had the highest frequency? • Answer : 3
- 23. Question • Which letter occurs the most frequently in the following sentence? THE SUN ALWAYS SETS IN THE WEST. Answer : S
- 24. Fifty students of B.A. (Major) course obtained the following scores in an achievement test. Tabulate the data in a frequency distribution table
- 25. Activity time
- 26. Answers In the above example, the total no. of scores=50, • Highest score=68 • Lowest score=21 • Range=68-21=47 • Hence, here 10 classes are sufficient. • i=47/10=4.7 (approx.5)
- 28. Graphing Data Three types of graphs. • Frequency polygon • Bar graph • Histogram • Smooth curve
- 29. Favorite Type of Movie 1 Comedy 6 Action 4 Romance 3 Drama 8 SciFi 2 0 1 2 3 4 5 6 7 8 9 Comedy Action Romance Drama SciFi
- 30. The bar graph shows the results when a die was thrown a number of times. How many sixes were thrown?
- 31. Take marker and write “something” on the board.
- 32. Calculating Mid Point For Frequency Polygon
- 33. Guideline For Constructing A Frequency Polygon
- 34. Smooth Curve Follow these two guidelines in constructing smooth curves: • Be sure your score axis increases from left to right. • Be sure the “tails” or ends of the curves come close to, but do not touch, the baseline.
- 35. Cont.….
- 36. Two Major Characteristics Of Distribution Symmetrical • Each half of the distribution is a mirror image of the other side. Asymmetrical • This type f distribution has no matching sides.
- 37. Check list • Statistics • List • Simple frequency distribution • Grouped frequency distribution • Range • Interval • Lower limit • Upper limit • Frequency • Midpoint • Histogram • Frequency polygon • Smooth curve • Symmetrical distribution • Normal distribution • Positively skewed distribution • Negatively skewed distribution
- 38. Percentiles • Percentile: the value below which a percentage of data falls. Example: You are the fourth tallest person in a group of 20 80% of people are shorter than you: That means you are at the 80th percentile. Formula : R = P / 100* (N+1)
- 39. Example • Find P25 and P50 in the following distribution of scores. 115, 112, 110, 108, 106, 104, 100, 100, 98, 96, 96, 94, 93, 91, 90, 88 • Answer: P25= 93.5 , P50= 99 • Formula : R = P / 100 (N+1)
- 40. Measures Of Central Tendency • Mean • Median • Mode Mean Median Mode The "average" number The middle number The most frequent number
- 41. Mean Mode Median
- 42. Mean • The arithmetic mean is the sum of all of the data points divided by the number of data points.
- 43. Example Find the mean of this data: 1, 2, 4, 5 1+2+4+5=12 12/4 Answer = 3
- 44. Count …. • Question What is the mean of these values?
- 45. Count …. • Answer • Mean = (38 + 39 + 43 + 46 + 52 + 58 + 62 + 62 + 57 + 51 + 44 + 42) ÷ 12 = 594 ÷ 12 = 49.5°F
- 46. Median • The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger. • To find the median: 1. Arrange the data points from smallest to largest. 2. If the number of data points is odd, the median is the middle data point in the list. 3. If the number of data points is even, the median is the average of the two middle data points in the list.
- 47. Count …. • Example 1 • 1,2,3,4,5 • Median is 3 • Example 2 • 0,1,2,3,4,5 • 2+3/2 = 5/2 • Median is 2.5
- 48. Activity month Jan Feb March April May June July Aug Sep Oct Nov Dec Temp 38 39 43 46 52 58 62 62 57 51 44 42 What is the median of these values?
- 49. Answer • The median is the "middle" value First arrange the temperatures in order: 38, 39, 42, 43, 44, 46, 51, 52, 57, 58, 62, 62 There are two temperatures in the middle: 46°F and 51°F So the median is the mean of them = (46 + 51) ÷ 2 = 48.5°F
- 50. Mode • The mode is the most commonly occurring data point in a dataset. • The mode is useful when there are a lot of repeated values in a dataset. • There can be no mode, one mode, or multiple modes in a dataset. Example : 0,1,2,5,7,9,3,1,0,5,1,3,2,1,1 Answer 1
- 51. Activity What is the mode of these values?
- 52. Count …. Answer The mode is the most frequently occurring average temperature = 62°F in July and August.
- 53. Skewed Data • Data can be "skewed", meaning it tends to have a long tail on one side or the other: • Negative Skew • No Skew • Positive Skew https://www.mathsisfun.com/data/skewness.html
- 54. Count ….
- 57. Activity Time
- 58. Question • Find the mean, median, mode, and range for the following list of values: 1) 13, 18, 13, 14, 13, 16, 14, 21, 13 2) 1, 2, 4, 7
- 59. Activity time
- 60. Answer key Mean: 15 Median: 14 Mode: 13 Range: 8 ==================== Mean: 3.5 Median: 3 Mode: None Range: 6
- 61. Draw a perfect bell curve.
- 63. Thank you