Probability and statistics (frequency distributions)
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- Frequency distributions organize and summarize data by grouping it into classes and counting the frequency of observations in each class. They can be presented in tables or graphically. - Common graphical representations include histograms, relative frequency histograms, frequency polygons, and ogives. - Categorical frequency distributions are used for nominal or ordinal data by tallying the frequency of observations in each category.
Probability and statistics (frequency distributions)
- 2. Charts and Frequency Distributions
- 3. When the variable of interest is qualitative, the statistical table is a list of the categories being considered along with measure of how often each value occurred. The measure can be presented in the following way:The frequency or number of measurements in each categoryThe relative frequency, or proportion of measurements in each categoryThe percentage of measurement in each category
- 4. Example1. 4000 freshmen were admitted in Don Bosco Technical College in Mandaluyong for the school year 2010-2011. The Students were enrolled in the following program:
- 5. Bar GraphUses the height of the bar to display the amount in a particular category.Pie ChartDisplays how the total quantity is distributed among the categories.
- 6. When a quantitative variable is recorded over time at equally spaced intervals, the data set forms a time series. Time series data are most effectively presented on a line chart.
- 7. Example. Table that shows the daily production of Gardenia BreadLine Graph
- 8. Stem and Leaf PlotA stem and leaf plot presents a graphical display of the data using the actual numerical values of each data point.
- 9. Steps in constructing:Divide each measurement into two parts: stem and leafList the stem in column, with a vertical line to the right.For each measurement, record the leaf portion in the same row as its corresponding stem.Order the leaves from lowest to highest in each stem.
- 10. Example Daily sales of desktop computers of JRC Computer Company for 40 days.
- 12. Frequency DistributionSteps in Constructing a Frequency Distribution TableDetermine the number of classes by using Sturges’ Formula: K = 1 + 3.322 log n = approximate number of classes n = number of observations2. Determine the approximate class size. Whenever possible, all classes should be of the same size. The following steps can be used to determine the class size:* Solve for the range, R = max- min*Compute for C’ = R / K *Round-off C’ to a convenient number(nearest whole number)
- 13. Frequency DistributionSteps in Constructing a Frequency Distribution Table3. Determine the lowest class limit. The first class must include the smallest value in the data set.Determine all class limits by adding the class size , C, to the limit of the previous class.Tally the frequencies for each class. Sum the frequencies and check against the total number of observations.
- 14. ExampleConstruct a frequency distribution from the final grades of Stat 101 Students given below:SolutionConstruct a stem and leaf plot.
- 15. The Complete Frequency Distribution Table
- 16. Graphical Representation of a Frequency DistributionFrequency Histogram – a bar graph that displays the classes on the horizontal axis and frequencies of the classes on the vertical axis; the vertical lines of the bars are erected at the class boundaries and the height of the bars correspond to the class frequency.Relative Frequency Histogram – a graph that displays the classes on the horizontal axis and the relative frequencies on the vertical axis.
- 17. Graphical Representation of a Frequency Distribution3. Frequency Polygon – a line chart that is constructed by plotting the frequencies at the class marks and connecting the plotted points by means of straight lines; the polygon is closed by considering an additional class at each end and the ends of the lines are brought down to the horizontal axis at the midpoints of the additional classes.Ogives – graphs of the cumulative frequency distribution.< ogive – the <CF is plotted against the UCB> ogive – the >CF is plotted against the LCB
- 18. Categorical Frequency DistributionThe Categorical frequency distribution is used for data that can be placed in specific categories, such as nominal or ordinal-level data.ExampleTwenty five students were given the following grades. The data set is: C A B A D F B A C A C D F B B A B D F C B C C B D
- 19. SolutionMake a table with A, B, C, D, and F as classes.Tally the data and count the tallies.Find the percentage of values in each class by using the formulaFind the total frequency and percent .
- 20. Table of frequency and percent