Frequency-Distribution..m.,m.........pptx

Math

1. Distribution Frequency

2. The frequency is how often a value occurs in an interval, while distribution is the pattern of frequency of the variable. What is Frequency Distribution?

3. A frequency distribution is the pattern of frequencies of a variable. It’s number of times each possible value of a variable occurs in a data set.

4. A frequency distribution are depicted using graphs and frequency tables.

5. Types of Frequency Distribution 1.Ungrouped 2. Grouped 3. Relative 4. Cumulative

6. 1. Ungrouped Frequency Distribution is a type of frequency distribution that displays the frequency of each individual data value instead of groups of data values. We can directly see how often different values occurred in the table.

7. You can use this type of frequency distribution for categorical variables.

8. Create a table with 2 columns. First column is for the “name” of label and the second column is for “frequency.” For ordinal variables, the values should be ordered from smallest-largest in the table rows. How to make an ungrouped frequency table?

9. 2. Count the frequencies. The frequencies are the number of times each value occurs. Especially if your dataset is large, it may help to count the frequencies by tallying. Add third column called “tally. ”

10. Example #1: A gardener set up a bird feeder in their backyard. To help them decide how much and what type of birdseed to buy, they decide to record bird species that visit their feeder. Over the course of one morning, the following birds visit their feeder.

11. Bird Species Tally Marks Frequency Chickadee III 3 Dove I 1 Finch IIII 4 Grackie II 2 Sparrow IIII 4 Starling II 2

12. Example #2: 4 families had 1 pet 3 families had 2 pets 2 families had 3 pets 1 family had 4 pets

13. Solution: Number of Pets Frequency 1 4 2 3 3 2 4 1

14. Take note that ungrouped frequency distributions work best with small datasets in which there are only a few unique values.

15. 2. Grouped Frequency Distribution The number of observations of each class interval of a variable. Class intervals are ordered groupings of a variable’s values. You can use this type of frequency distribution for quantitative variables.

16. How to make a grouped frequency table? 1. Divide the variable into class intervals. Calculate the range. Subtract the lowest value in the dataset from the highest. Decide the class interval width. There are no firm rules on how to choose the width but the following formula is a rule of thumb.

17. width   You can round this value to a whole number or a number that’s convenient to add (such as a multiple of 10) Calculate the class intervals. Each interval is defined by a lower limit and upper limit. Observation in a class interval are greater than or equal to the lower limit and less than the upper limit: Lower limit < x < upper

18. The lower limit of the first interval is the lowest value in the dataset. Add the class interval width to find the upper limit of the first interval and the lower limit of the second variable. Keep adding the interval width to calculate more class intervals until you exceed the highest value.

19. 2. Create a table with two columns and as many rows as there are class intervals. Label the first column using the variable “name” and label the second column “frequency.” Enter the class intervals in the first column. 3. Count the frequencies. The frequencies are the number of observations in each class interval.

20. Example : A sociologist conducted a survey of 20 adults. She wants to report the frequency distribution of ages of the survey respondents. The respondents were the following ages in years. 52, 34, 32, 29, 63, 40, 46, 54, 36, 36, 24, 19, 45, 20, 28, 29, 38, 33, 49, 37

21. Range= highest – lowest Range= 63-19 Range= 44 width width Width= 9.84  

22. Example #2:

23. 3. Relative Frequency Distributions The proportion of observations of each value or class interval of a variable. You can use this type of frequency distribution for any type of variable when you’re more interested in comparing frequencies than the actual number of observations.

24. How to make a relative frequency table? 1. Create an ungrouped or grouped frequency table. 2. Add a third column to the table for the relative frequencies. To calculate the relative frequencies, divide each frequency by the sample size. The sample size is the sum of the frequencies.

25. Relative Frequency Formula Relative frequency Or Relative frequency where, f is the number of times the data occurred in an observation N= total frequency  

26. Example :

27. From this table, the gardener can make observations, such as that 19% of the bird feeder visits were from chikadees and 25% were from finches and sparrow.

28. The sum of the frequencies less than or equal to each value or class interval of a variable. You can use this type of frequency distribution for ordinal or quantitative variables when you want to understand how often observations fall below certain values. 4. Cumulative Frequency Distributions

29. 1. Create an ungrouped or grouped frequency table for an ordinal or quantitative variable. Cumulative frequencies don’t make sense for nominal variables because the values have no order, one value isn’t more than or less than another value. 2. Add a third column to the table for the cumulative frequencies. The cumulative frequency is the number of observations less than or equal to a certain value or class interval. How to make a cumulative frequency table?

30. To calculate the relative frequencies, add each frequency to the frequencies in the previous rows. 3. Optional: If you want to calculate the cumulative relative frequency, add another column and divide each cumulative frequency by the sample size.

31. Example:

32. From this table, the sociologist can make observations such as 13 respondents (65%) were under 39 years old, and 16 respondents (80%) were under 49 years old.

33. A. Direction: Answer the following question by filling the blank with the correct answer. Choose your answer in the box below. Activities: Frequency Distribution Ungrouped Frequency Distribution Grouped Frequency Distribution Relative Frequency Distribution Cumulative Frequency Distribution

34. ______1. This type of frequency distribution can be used for categorical variables. ______2. You can use this type of frequency distribution for any type of variable such as comparing frequencies than the actual number of observations.

35. ______3. It describes the number of observations for each possible value of a variable using graphs and frequency tables. ______4. This type of frequency distribution refers to the sum of frequencies less than or equal to each value or class interval of a variable.

36. ______5. Another type of frequency distribution that can be used for quantitative variables.

37. B. Analyze and answer the following problems using ungrouped, grouped, relative and cumulative frequency distribution. 1. The marks obtained by the Grade 2 pupils in Mathematics test are given as: 52, 46, 92, 78, 62, 44, 34, 46, 58, 52. Prepare an ungrouped frequency table for the data.

38. 2. The ages of 30 people in your locality is 5, 65, 62, 48, 5, 23, 17, 40, 30, 30, 30, 51, 5, 17, 17, 39, 23, 48, 40, 65, 65, 62, 5, 5, 17, 62, 51, 23, 48, 40. The age ranges from 5 to 65. 3. Solve the problem below for the relative frequency.

39. Name of Car Frequency Relative Frequency Honda 7 Toyota 3 Hyundai 5 Mitsubishi 5 Suzuki 6 Ford 7 BMW 9

40. 4. A basketball coach had each player on the team shoot ten free throws, and he kept track of how many free throws each player made. Find the cumulative frequency of the free throws made by each basketball player.

41. Free throws made Frequency Cumulative Frequency 3 1 5 1 8 2 2 4 6 2

42. Thank you!