3 Frequency Distribution biostatistics wildlife
- 2. • Data in original form- raw data. • Raw data is not very meaningful to an audience. • Raw data has to be organized to draw inferences and conclusions • Repetition of number in a data set is termed as frequency of that particular number or the variable • The frequencies of variables in a data are to listed in a table • A frequency distribution is the organizing of raw data in table form, using classes and frequencies. • Table is frequency distribution table
- 3. • To organize data in a meaningful, intelligible way • To enable the reader to determine the nature or shape of the distribution • To facilitate computational procedures for measures of average and spread • To enable us to draw charts and graphs for the presentation of data • To enable the reader to make comparisons among different data sets Reasons for Constructing a Frequency Distribution
- 4. Types • Categorial frequency distribution • Ungrouped frequency distribution • Grouped frequency distribution • Cumulative frequency distribution • Relative frequency distribution • Relative cumulative frequency distribution
- 5. • Categorical frequency distributions - used for data that can be placed in specific categories political affiliation, religious affiliation, supporters of Clubs, Members of Associations, blood type etc. Blood Type Frequency Distribution
- 6. • Ungrouped Frequency Distributions- used for data that can be enumerated and when the range of values in the data set is not large. Kilometers you (all) have to travel from home to campus, number of animals in quadrates Kilometer travelled frequency distribution
- 7. • Grouped frequency distributions - used when the range of values in the data set is very large. The data must be grouped into classes that are one unit or more in width. limits Class Boundaries 24 - 37 23.5 - 37.5 4 38 - 51 37.5 - 51.5 14 52 - 65 51.5 - 65.5 7 Frequency ◦Lower Class Limit (LCL) is the smallest data value that can be included in the class ◦Upper Class Limit (UCL) is the largest data value that can be included in the class ◦Class Boundaries are used to separate the classes so that there is no gaps in the frequency distribution Rule of Thumb: Have one additional place value and end in .5 Find class boundaries by subtracting 0.5 from each LCL and adding 0.5 to each UCL Frequency of fishes of different size classes
- 8. One must decide how many classes to use and the width of each class using the following guidelines: ◦ There should be between 5 and 20 classes. ◦ The classes must be mutually exclusive (non overlapping values) ◦ The classes must be continuous (no gaps, even if frequency is 0) ◦ The classes must be exhaustive (use all the data) ◦ The classes must be equal in width
- 9. In a survey of 20 patients who smoked, the following data were obtained. Each value represents the number of cigarettes the patient smoked per day. Construct a frequency distribution using six classes Number of cigatrete smoked by each: 5,11,6,11,10,8,6,14,23,13,17,19,11,9,18,14,13,12,15,15 • Step 1: Find the highest and lowest values: H = 23 and L = 5. • Step 2: Find the range: R = H – L = 23 – 5 = 18. • Step 3: Select the number of classes = 6. • Step 4: Find the class width by dividing the range by the number of classes. Width = 18/6 = 3. (if fraction rounded up to next whole value). • Step 5: Select a starting point for the lowest class limit. This value is 5. The lower-class limits are 5, 8, 11, 14, 17 and 20. • Step 6: The upper-class limits are 7, 10, 13, 16, 19 and 22. (8 - 1, etc). • Step 7: Find the class boundaries by subtracting 0.5 from each lower-class limit and adding 0.5 to the upper-class limit. • Step 8: Tally the data, write the numerical values for the tallies in the frequency column and find the cumulative frequencies.
- 10. Class Limits Class Boundaries Frequency Cumulative frequency 5 – 7 4.5 – 7.5 2 2 8 – 10 7.5 – 10.5 3 5 11 – 13 10.5 – 13.5 6 11 14 – 16 13.5 – 216.5 5 16 17 – 19 16.5 – 19.5 3 19 20 – 22 19.5 – 22.5 1 20 Cumulative Frequency Distribution Cumulative frequency defined as the sum of all previous frequencies up to the current point. The cumulative frequency for each class interval is the frequency for that class interval added to the preceding/succeeding classes. If cumulative frequencies are represented in a Table then it is called as cumulative frequency distribution
- 11. Two types Less than: In this frequency distribution, the frequencies of all preceding classes are added to the frequency of a class. It is constructed by adding the first-class frequency to second class frequency that to the third-class frequency and so on. More than: The frequencies of succeeding classes are added to the frequency of a class. It is constructed by subtracting the first class frequency from the total, second class frequency from that and so on. Class Limits Cumulative frequency Less than 7 2 Less than 10 5 Less than 13 11 Less than 16 16 Less than 20 19 Less than 22 20 Class Limits Cumulative frequency More than 5 20 More than 8 18 More than 11 17 More than 14 9 More than 17 4 More than 20 1
- 12. • Cumulative Relative Frequency Distribution – Relative frequency is the ratio of the cumulative frequency to the size of the sample. – The relative cumulative frequency is the cumulative frequency for that class interval added to the preceding cumulative total. Class Limits Class Boundaries Frequency Relative Frequency Cumulative frequency Relative Cumulative frequency 5 – 7 4.5 – 7.5 2 0.10 2 0.10 8 – 10 7.5 – 10.5 3 0.15 5 0.25 11 – 13 10.5 – 13.5 6 0.30 11 0.55 14 – 16 13.5 – 216.5 5 0.25 16 0.80 17 – 19 16.5 – 19.5 3 0.15 19 0.95 20 – 22 19.5 – 22.5 1 0.05 20 1.00
Editor's Notes
- #5: Nominal data: a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories can be ordered in terms of occurrence / priority