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 Amsco Integrated Algebra I: Measures of Central Tendency and Grouped Data
This is a free lesson from our course in Amsco's Integrated Algebra
In this lesson you'll learn the basic concpts of measures of central tendency. It also explains how do the various measures of central tendency compare with each other. When some data is colleted, we have certain numbers which represent the characteristics of the data, around which the data appears to be concentrated; we call such numbers as the measures of central tendency. There are three most commonly used measures of central tendency .i.e. mean, mode and median for grouped data, for which the basics you have already learnt earlier. The mean is typically what is meant by the word average and median is the value which divides the values into two equal halves, with half of the values being lower than the median and half higher than the median E.g. the mean of 7, 12, 24, 20, 19 is 16.4 and median of the same five numbers is 19. (More text below video...)
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(Continued from above) Mode is the most frequently-occurring value (or values) i.e. the mode is the value (or values) with the highest frequency E.g. for individuals having the ages in the group-18, 18, 19, 20, 20, 20, 21, and 23: the mode is 20.
As noted above, the mode is the value of the interval that contains the greatest frequency and the median is the value of the interval that contains the middle value. In general; to find the mean for N values in a table of grouped data with the length of each interval I, the procedure is:
• for each interval, multiply the interval value by its corresponding frequency.
• find the sum of these products.
• divide the sum by total frequency. In cases where interval if other then length l: We will simply identify the intervals and work out modal interval i.e. group of numbers (unlike mode which is usually a single number). The modal interval is the interval that contains the greatest frequency. Both the mode and the modal interval depend on the concept of greatest frequency, but for the modal interval, we look for the interval that has the greatest frequency. The video above will explain in detail with the help of several examples.


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