lesson 3

• Measures of Central Tendency

  Described and obtained after summarizing into measurements like average or measures of central tendency
• Central Tendency


  A statistical measure to determine a single score that defines the center of a distribution. The goal of central is to find the single score that is most typical or most representative of the entire group
• Three Major Types of Central Tendency

  • Mean
  • Median
  • Mode
• Mean


  The mean or arithmetic mean is the arithmetic average of a set of observations
• Calculating Mean (Ungrouped Data)

  Sum of all values divided by the total frequency
• Weighted Mean


  A mean calculated by giving different weights to different values
• Calculating Weighted Mean

  Sum of (each of the item values x weight of each item) divided by sum of weights
• Midpoint Method


  A method to calculate mean from grouped data using the midpoint of each class interval
• Unit Deviation Method


  A method to calculate mean from grouped data using the unit deviation from an assumed mean
• Class Interval

  • 70-75
  • 76-81
  • 82-87
  • 88-93
  • 94-99
  • 100-105
  • 106-111
  • 112-117
  • 118-123
• Frequency (f)

  • 2
  • 7
  • 20
  • 21
  • 39
  • 27
  • 14
  • 10
  • 5
• Cumulative Frequency (cf)

  • 2
  • 9
  • 29
  • 50
  • 89
  • 116
  • 130
  • 140
  • 145
• Calculating Median (Grouped Data)

  1. Get the Median Class

  2. Determine cfb

  3. Determine the lower boundary of the median class

  4. Frequency of median class

  5. Class Size

  6. Median = Xlb + (n/2 - cfb)/fm * c
• Median


  Single value from the data set that measures the central item in the data
• The frequency distribution of the test results of 100 BS Math Students in Statistical Analysis
• Class Interval

  • 15-24
  • 25-34
  • 35-44
  • 45-54
  • 55-64
  • 65-74
  • 75-84
  • 85-94
• Frequency (f)

  • 5
  • 10
  • 11
  • 23
  • 26
  • 14
  • 8
  • 3
• Cumulative Frequency (cf)

  • 5
  • 15
  • 26
  • 49
  • 75
  • 89
  • 97
  • 100
• Mode


  Observation or value which appears the most number of times in the set of values
• The results of the IQ test of a group of Psychology students in certain college are presented in a frequency distribution
• Calculating Mode (Grouped Data)

  1. Find the modal class

  2. Determine the class size

  3. Get the fm1 and fm2

  4. Mode = Xlb + (fm1 / (fm1 + fm2)) * c