Frequency Distribution and Variation

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# Frequency Distribution and Variation - PowerPoint PPT Presentation

Frequency Distribution and Variation. Prepared by E.G. Gascon. Frequency Distributions. Frequency distribution: Quantitative Data is a table that shows classes or intervals (frequency f of a class is the number of data entries in the class

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### Frequency Distribution and Variation

Prepared by E.G. Gascon

Frequency Distributions
• Frequency distribution: Quantitative Data is a table that shows classes or intervals (frequency f of a class is the number of data entries in the class
• Lower class limit = least number that can belong to the class
• Upper class limit = greatest number that can belong to the class
• Class width = distance between lower (or upper) limits of consecutive classes. (Not- lower-upper within a class)
• Range – difference between the maximum and minimum data
• Class boundaries- are the numbers that separate classes without forming gaps between them
Constructing a Frequency Distribution
• Decide on the number of classes (could be arbitrary)
• Find the range= highest value – lowest value
• Find the class width = Divide the range by number of classes (round up to next whole number if decimal)
• Decide the class limits
• Tally
• Count tally to find frequency
• Total frequency
Creating a Histogram in Excel

There are several ways depending upon the version

Household Income Example

• Enter the data (Midpoint as text by writing each with a ‘ in front ex: ‘250
• Select the Select the data and create a column
Creating a Histogram in Excel-p2
• Make the bars touch by changing the “gap width= 0” Right click on the bars and select “Format Data Series”
Measures of Central Tendency
• Mean: sum of the data divided by number of entries
• Affected by outliers (values which are a distance from the majority of entries
• Median: Middle of data when the data set is ordered.
• If the data set has an odd number of entries median is the middle data entry.
• If the data set is even number of entries, the median is the mean of the two middle entries.
• Mode: is the data entry that occurs with the greatest frequency.
• If no entry is repeated, the data set has no mode.
• If two entries occur with the same greatest frequency, each entry is a mode and the data set is called bimodal.
• The mode is the only measure of that is used to describe data non-numeric data, when working with quantitative data, it is rarely used.
Measures of Variation
• Range: is the difference between the maximum and minimum data entries in the set.
• Deviation: of an entry x, in a population data set is the difference between the entry and the mean of the data set
• Variance is the average of the sums of all the deviations. (not easily calculated in a large sample so….

Population variance:

• Sample variance:
• Sample Standard Deviation:
Interpretation of the Standard Deviation
• The size of the standard deviation tells up something about how spread out the data are from the mean.
• ~68% of the data lie within 1 standard deviation of the mean (1 times the size of the SD on either side of the mean)
• ~95% of the data lie within 2 standard deviation of the mean(2 times the size of the SD on either side of the mean)

~99.7% of the data lie within 3 standard deviation of the mean(3 times the size of the SD on either side of the mean)

Standard Score, (z-score) represents the number of standard deviations a given value x falls from the mean .