Statistics (4th quarter)

• Measure of central tendency


  A single value that represents a data set, with the purpose of locating the center of the data set
• The arithmetic mean, often called the mean, is the most frequently used measure of central tendency. It is the only measure in which all values play an equal role, and it is appropriate for interval or ratio data.
• Properties of Mean

  A set of data has only one mean
• Mean for Ungrouped Data

  1. Mean = Sum of all values / Number of Values

  2. Sample Mean: x bar = (sum of x) / n

  3. Population Mean: μ = (sum of x) / N
• Sample Mean for Grouped Data

  x bar = (sum of fx) / n
• Population Mean for Grouped Data

  μ = (sum of fx) / N
• Median


  The midpoint of the data array, the value that separates the upper half of the distribution from the lower half
• The median is unique, there is only one median for a set of data?


  properties of median
• If n is odd, the median is the middle ranked
• Median for Grouped Data

  Median (Ranked Value) = LB + (N/2 - cf) / f * i
• Mode


  The value in the data set that appears most frequently. A data may not contain any mode if none of the values is "most typical".
• Types of Mode?

  Unimodal, Bimodal, Trimodal, Multimodal, No Mode
• Unimodal - one value that occurs most frequently
• Bimodal - two values with the greatest frequency
• Trimodal - three values with the greatest frequency
• Multimodal - more than three values with the greatest frequency
• No Mode - all values have the same frequencies
• Mean can be applied for interval or ratio data


  properties of mean
• All values in the data set are included in computing the mean


  properties of mean
• The mean is very useful in comparing two or more data sets


  properties of mean
• Mean is affected by the extreme small or large values on the data set


  properties of mean
• The mean cannot be computed for the data in a frequency distribution with an open-ended class


  properties of mean
• Mean is most appropriate in symmetrical data?


  properties of mean
• The median is found by arranging the set of data in ascending or descending form and getting the value of the middle observation?

  Properties of Median
• Median is not affected by the extreme small or large values?


  • Properties of Median

• Median can be computed for ordinal, interval and ratio data?

  Properties of median

• Median is appropriate in a skewed data?

  Properties of Median
• If n is even, the median is the average of the two middle ranked values
• Median (Rank Value) = (n+1) / 2