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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

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frequency distributions
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
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
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
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
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
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
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 .