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Sample Size and Frequency Distribution
- 3. MS. SARAH GEVERO FORMENTO
- 5. POPULATION Is any complete group with at least one characteristic in common. Population are not just people. Populations may consist of, But are not limited to, people, animals, busin buildings, motor vehicles, farms, objects or http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-
- 7. For example, if the researcher wants to get 95% precision, he must tolerate 5% error, Now if the population size is 1,500 pupils, how he needs in his study? Given: N=1,500 e=.05 N= 1,500 1+1,500(.05)2 N=1,500 1+3.75 N=315.8 pupils The sample size is 316 pupils with 95% precision.
- 8. As to minimum sample size, Gay(1976) has to say: For descriptive research, a sample of 10% of the population is considered. For smaller population, 20% maybe required. For correlational studies atleast 30 subjects are needed to establish the existence or non-existence of a relationship. For casual-comparative studies and many experimental studies, a minimum of 30
- 12. Seatwork: Individual 2. The population is 160 mathematics Major of ABC College. The following table shows the year level and the number of male and female students. Using the stratified random sampling, compute the number of sample in each year level and the number of male and female in each level. Explain sampling method to select from each stratum where n=80. Year level Male Female Total 1 30 20 50 2 25 20 45 3 28 12 40 4 15 10 25 Total 98 62 160
- 13. Textual Method -data are presented in paragraph form. The text should emphasize the importance of the figures and its relevance to other figure(Bernardo, 2012).
- 14. Example: “The country’s virgin forest is down to less than one million hectares from 16M hectares in 1936. Thus, climatic changes have become more pronounced and detrimental to food crops while potable water resources which are also sources of cheap and clean power and energy are dying
- 15. Data represented in columns and rows as compared to textual form, tabular form is much briefer, easy To comprehend and more convenient. FREQUENCY DISTRIBUTION -data maybe ungrouped data or grouped data. Types of Frequency: Absolute(f), relative or cumulative(‘less than or
- 16. The distribution or table of frequencies is a table of the statistical data with its corresponding frequencies. Absolute frequency: number of times that a value appears. It is represented as where the subscript represents each of the values. The sum of the absolute frequencies is equal to the total number of data, represented bas equivalent to: F1+f2+f3+…+fn=N
- 17. Relative frequency: the result of dividing the absolute frequency of a certain value by the total number of data. It is represented as . The sum of the relative frequencies is equal to . We can prove this easily by factorizing . Cumulative frequency: the sum of absolute frequencies of all the values equal to or less than the considered value. This is represented as . Ni= fi N Relative cumulative frequency: the result of dividing the cumulative frequency by the total number of information, which is represented by
- 18. Example 15 students answer the question of how many brothers or sisters they have. The answers are 1,1,2,0,3,2,1,4,2,3,1,0,0,1,2 Then, we can construct a table of frequenciesBrother s Absolute Frequency fi Relative Frequency Ni Cumulative frequency Fi Relative Cumulative Frequency Ni 0 3 3/15 3 3/15 1 5 5/15 3+5=8 3/15+5/15=8/15 2 4 4/15 3+5+4=12 12/15 3 2 2/15 3+5+4+2=14 14/15 4 1 1/15 3+5+4+2+1=15 15/15 Total 15 1
- 27. a.Graphs 0r Chart 1. Line Graph 2. Multiple Line Graphs 3. Bar Graph 4. Pie Chart 5. Pictograph 6. Steam and Leaf Graph Display
Editor's Notes
- Important to clearly identify the population being studied or referred to, so that you can understand who or what are be included in the data.
- Notice that the difference between the cumulative frequency and the relative frequency is only that in the case of the relative we must divide by the total number of data. This can help us avoid unnnecessary calculations.
- Collect your data. Unless you are just completing a math homework assignment, calculating relative frequency generally implies that you have some form of data. Conduct your experiment or study and collect the data. Decide how precisely you wish to report your results. Sort the data. After you complete your study or experiment, you are likely to have a collection of data values that could look like 1, 2, 5, 4, 6, 4, 3, 7, 1, 5, 6, 5, 3, 4, 5, 1. In this form, the data appear almost meaningless and difficult to use. It is more helpful to sort the data in order from lowest to highest. This would result in the list 1,1,1,2,3,3,4,4,4,5,5,5,5,6,6,7.[1]When you are sorting and rewriting your collection of data, be careful to include every point correctly. Count the data set to make sure you do not leave off any values.
- Use a data table. You can summarize the results of your data collection by creating a simple data frequency table. This is a chart with three columns that you will use for your relative frequency calculations. Label the columns as follows:[2]{\displaystyle x}. This column will be filled with each value that appears in your data set. Do not repeat items. For example, if the value 4 appears several times in the list, just put {\displaystyle 4} under the {\displaystyle x} column once. {\displaystyle n}, {\displaystyle n(x)} or {\displaystyle fr(x)}. In statistics, the variable {\displaystyle n} is conventionally used to represent the count of a particular value. You may also write {\displaystyle n(x)}, which is read as “n of x,” and means the count of each x-value. A final alternative is {\displaystyle fr(x)}, which means the “frequency of x.” In this column, you will put the number of times that the value appears. For example, if the number 4 appears three times, you will place a 3 next to the number 4. Relative Frequency or {\displaystyle P(x)}. This final column is where you will record the relative frequency of each data item or grouping. The label {\displaystyle P(x)}, which is read “P of x,” could mean the probability of x or the percentage of x. The calculation of relative frequency appears below. This column will be used after you complete that calculation for each value of x.
- Count your full data set. Relative frequency is a measure of the number of times a particular value results, as a fraction of the full set. In order to calculate relative frequency, you need to know how many data points you have in your full data set. The will become the denominator in the fraction that you use for calculating.[3]In the sample data set provided above, counting each item results in 16 total data points.
- Count each result. You need to determine the number of times that each data point appears in your results. You may want to calculate the relative frequency of one particular item, or you may be summarizing the overall data for the full data set.[4]For example, in the data set provided above, consider the value {\displaystyle 4}. This value appears three times in the list.
- Divide each result by the total size of the set. This is the final calculation to determine the relative frequency of each item. You can set it up as a fraction or use a calculator or spreadsheet to perform the division.[5]Continuing with the example above, because the value {\displaystyle 4} appears three times, and the full set contains 16 items, you can determine that the relative frequency of the value {\displaystyle 4} is 3/16. This is equal to a decimal result of 0.1875. Present your results in a frequency table. The frequency table that you began above can be used to present the results in a format that is easy to review. As you perform each of the calculations, fill in the results in the corresponding places in the table. It is common to round your answers to two decimal places, although you will need to decide this for yourself based on the needs of your study. Because of rounding the end result may total something close to , but not exactly 1.0.[6]For example, using the data set above, the relative frequency table would appear as follows: x : n(x) : P(x) 1 : 3 : 0.19 2 : 1 : 0.06 3 : 2 : 0.13 4 : 3 : 0.19 5 : 4 : 0.25 6 : 2 : 0.13 7 : 1 : 0.06 total : 16 : 1.01
- Report items that do not appear. It may be just as meaningful to report items whose frequency is 0 as to report those items that do appear in your data set. Look at the kind of data you are collecting, and if you notice any gaps in your sorted data, you may need to report them as 0s.For example, the sample data set you have been working with includes all values from 1 to 7. But suppose that the number 3 never appeared. That could be important, and you would report the relative frequency of the value 3 as 0.
- Show your results as percentages. You may wish to turn your decimal results into percentages. This is a common practice, as relative frequency is often used as a predictor of the percentage of times that some value will occur. To convert a decimal number to a percentage, simply shift the decimal point two spaces to the right, and add a percent symbol.For example, the decimal result of 0.13 is equal to 13%. The decimal result of 0.06 is equal to 6%. (Don’t just skip over the 0.)
- See p. 29 by Bernardo 2012.