stats Frequency Distribution

1. Frequency Distribution

2. Frequency Distribution A representation, in a tabular format, which displays the number of observations within a given interval. The intervals must be mutually exclusive (each score must belong to exactly one class) and exhaustive (Including every possible element).

3. Question How do we construct a frequency distribution table?

4. Let’s Try!!! Ages of 50 men randomly selected from a population who died in gunfire are given. Construct a frequency distribution table having 7 classes.

5. 19 18 30 40 41 33 73 25 23 25 21 33 65 17 20 76 47 69 20 31 18 24 35 24 17 36 65 70 22 25 65 16 24 29 42 37 26 46 27 63 21 27 23 25 71 37 75 25 27 23

6. Determine the range. R = Highest Value – Lowest Value R = 76 – 16 = 60

7. Find the class width (c).

8. Write the classes starting with lowest score.

10. General Process of Constructing a Frequency Table STEP 1: Determine the range. Range (R)= Highest Value – Lowest Value Example in data: 29,55,65,23,45,86,44 Find Range

11. STEP 2.Determine the tentative number of classes (k) Note: These classes are usually specified in question. The number of classes should be between 5 and 20. The actual number of classes may be affected by convenience or other subjective factors.

12. STEP 3. Find the class width by dividing the range by the number of classes. (Always round – off )

13. STEP 4.Determine the frequency for each class by referring to the tally columns and present the results in a table.

14. When constructing frequency tables, the following guidelines should be followed. The classes must be mutually exclusive. That is, each score must belong to exactly one class. Include all classes, even if the frequency might be zero.

15. All classes should have the same width, although it is sometimes impossible to avoid open – ended intervals such as “65 years or older”. The number of classes should be between 5 and 20.

16. Using Table: What is the lower class limit of the highest class? Upper class limit of the lowest class? Find the class mark of the class 43 – 51. What is the frequency of the class 16 – 24?

17. SLOPE

18. SLOPE Slope is a measure of steepness

19. Types of Slope Zero Negative Positive Undefined or No Slope

20. If given 2 points on a line, you may find the slope using the formula m = y2 – y1 x2 – x1

21. Find the slope of the line through the points (3,7) and (5, 19). x1 y1 x2 y2 m = 19 – 7 5 – 3 m = 12 2 m = 6

22. Find the slope (3, 4) and (-6, -2)

23. If given an equation of a line, there are 2 ways to find the slope and y-intercept.

24. One method is to write the equation in slope-intercept form, which is y = mx + b. slope y-intercept

25. Find the slope and y-intercept of the following equations. y = 3x + ½ slope= 3 y-intercept = ½

26. 3x + 5y = 10 First, solve the equation for y. 3x + 5y = 10 5y = -3x + 10 y = -3/5 x + 2 m= -3/5 b = 2

27. Another method to find the slope if given an equation of a line is to write the equation in the form Ax + By = C. m = -A/B, b = C/B

28. Find the slope and y-intercept of the following equations. A B C 8x + 11y = 7 m= -8/11 b = 7/11

29. -6x = 2y + 14 First, rewrite the equation in the form Ax + By = C. -6x - 2y = 14 m= 6/-2 b = 14/-2 m= -3 b = -7

30. If given the graph of a line, find the slope by using the “triangle” method to find the rise over run.

31. rise = 4 m= rise run run = 5 m= 4/5

32. Feedback form MET’s Institute of Management, Bhujbal Knowledge City, Adgaon, Nashik 1. Name of the student: 2 . Graduation in: 3. Please tick whether you had learnt statistics in your graduation level: Yes No 4. Please grade yourself according to you in which category you lie in the knowledge of mathematics and statistics 1.Poor 2. Not good 3.Average 4.Good 5.Excellent

33. Whether Induction on basics of Mathematics and Statistics was fruitful for you ? Yes / No If Yes then please state why? Do you need any change in the current teaching methodology adopted for statistics? 7. Any suggestions related to the subject statistics:

34. The End