The document discusses measures of central tendency in the context of frequency distributions, focusing on how summary statistics can provide insights into data sets. It defines and explains various measures including arithmetic mean, geometric mean, and harmonic mean, and demonstrates their calculation with an example of customer accounts. The importance of these measures lies in their ability to represent the central point and trends within a data distribution.

1. MEASURES OF CENTRAL
TENDENCY
IN FREQUENCY DISTRIBUTIONS
UNIT II: DISTRIBUTION OF ONE-DIMENSIONAL
FREQUENCIES.
RBK

2. LEARNING OBJECTIVES
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3. SUMMARY STATISTICS
we constructed tables and graphs from raw
data. The resulting “pictures” of frequency
distributions illustrated trends and patterns in the
data. In most cases, however, we need more
exact measures. In these cases, we can use
single numbers called summary statistics to
describe characteristics of a data set. Central
tendency, and dispersion.
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Central Tendency: Central tendency is the middle point of a distribution.
Measures of central tendency are also called measures of location.

4. CALCULATING THE MEAN,
MEDIAN, AND MODE FROM
UNGROUPED DATA
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5. ARITHMETIC MEAN
We refer to the “average” of something.

6. THE GEOMETRIC MEAN 6
• Sometimes when we are dealing with quantities that change over a period of time, we need to know an
average rate of change, such as an average growth rate over a period of several years.
• Finding the growth rate: The geometric mean denotated as GM
The geometric mean is the average of a set of products,
the calculation of which is commonly used to determine
the performance results of an investment or portfolio

7. HARMONIC MEAN
The harmonic mean is the reciprocal of the average of reciprocals, the formula to define the harmonic
mean “HM” is given as follows:
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9. THE MODE

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CALCULATING THE MEAN,
MEDIAN, AND MODE FROM
GROUPED DATA

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In our sample of 600 customers, the
average monthly checking-account
balance is $142.25. This is our
approximation from the frequency
distribution.

13. To reach the(n + 1)/2 th. Because there are 600 accounts, the value for
(n + l)/2 is 300.5 (the average of the 300th and 301st items). The
cumulative frequency for the first two classes is only 78 + 123 = 201.
But when we moved to the third-class interval, 187 elements are added
to 201, for a total of 388. Therefore, the 300th and 301st observations
must be located in this third class (the interval from $100.00 to
$149.99)

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16. Mode class

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19. THANK YOU