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Properties of Mean, Median and Mode

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Management Accounting (BA 115)

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Listed booksIntroduction to Managerial AccountingWileyplus Stand-Alone to Accompany Isv Managerial Accounting
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Jason Bigata
University of the Philippines System
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Properties of Mean, Median and Mode

Properties of Mean

  1. Mean can be calculated for any set of numerical data.

  2. A set of numerical data has one and only one mean.

  3. Mean is the most reliable measure of central tendency since it takes into account every item in the set of data.

  4. The mean is affected by unusually large or small data values.

  5. The sum of the differences between individual observations and the mean is zero.

  6. The product of the mean and the number of items on which mean is based is equal to the sum of all given items.

  7. The sum of squares of deviation of set of values about its mean is minimum.

  8. If each item of the original series is replaced by the actual mean, then the sum of those substitutions will be equal to the sum of the individual items.

  9. Mean is not independent of change of origin and change of scale.

When to use the mean?

The mean is used when both of the following conditions are met:

  1. Data is scaled a) Data with equal intervals like speed, weight, height, temperature, etc.
  2. Distribution is normal b) The mean is sensitive to outliers that are found in skewed distributions, you should only use the mean when the distribution is more or less normal.

Properties of Median

  1. There is a unique median for each data set.

  2. It is not affected by extremely large or small values and is therefore a valuable measure of central tendency when such values occur.

  3. It is not applicable to qualitative data.

  4. Median is used when the data are ordinal.

  5. Median can determine by graphic method.

  6. The sum of the absolute deviations taken from the median is less than the sum of the absolute deviations taken from any other observation in the data.

When to use the median? The median is used when either one of two conditions are met. If the,

  1. Data is ordinal
  2. Distribution is skewed or non-normal.

Properties of Mode

  1. The mode is the easiest to compute.

  2. The mode is not always unique. A data set can have more than on mode, or the mode may not exist for a data set.

  3. Can be used for qualitative as well as quantitative data.

  4. Not affected by extreme values.

  5. The mode can be used when the data are nominal or categorical, such as religious preference, gender, or political affiliation.

  6. It cannot be manipulated algebraically: modes of subgroups cannot be combined.

When to use the mode?

The Mode is used when you want to know the most frequent response, number or observation in a distribution.

Properties of Mean, Median and Mode

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Properties of Mean, Median and Mode

Course: Management Accounting (BA 115)

50 Documents
Students shared 50 documents in this course

University: University of the Philippines System

Was this document helpful?
Properties of Mean, Median and Mode
Properties of Mean
1. Mean can be calculated for any set of
numerical data.
2. A set of numerical data has one and only
one mean.
3. Mean is the most reliable measure of
central tendency since it takes into
account every item in the set of data.
4. The mean is affected by unusually large
or small data values.
5. The sum of the differences between
individual observations and the mean is
zero.
6. The product of the mean and the
number of items on which mean is based
is equal to the sum of all given items.
7. The sum of squares of deviation of set of
values about its mean is minimum.
8. If each item of the original series is
replaced by the actual mean, then the
sum of those substitutions will be equal to
the sum of the individual items.
9. Mean is not independent of change of
origin and change of scale.
When to use the mean?
The mean is used when both of the following
conditions are met:
1. Data is scaled
a) Data with equal intervals like speed,
weight, height, temperature, etc.
2. Distribution is normal
b) The mean is sensitive to outliers that
are found in skewed distributions, you
should only use the mean when the
distribution is more or less normal.
Properties of Median
1. There is a unique median for each data
set.
2. It is not affected by extremely large or
small values and is therefore a valuable
measure of central tendency when such
values occur.
3. It is not applicable to qualitative data.
4. Median is used when the data are
ordinal.
5. Median can determine by graphic
method.
6. The sum of the absolute deviations taken
from the median is less than the sum of
the absolute deviations taken from any
other observation in the data.
When to use the median?
The median is used when either one of two
conditions are met. If the,
1. Data is ordinal
2. Distribution is skewed or non-normal.
Properties of Mode
1. The mode is the easiest to compute.
2. The mode is not always unique. A data
set can have more than on mode, or the
mode may not exist for a data set.
3. Can be used for qualitative as well as
quantitative data.
4. Not affected by extreme values.
5. The mode can be used when the data
are nominal or categorical, such as
religious preference, gender, or political
affiliation.
6. It cannot be manipulated algebraically:
modes of subgroups cannot be
combined.
When to use the mode?
The Mode is used when you want to know
the most frequent response, number or
observation in a distribution.
Properties of Mean, Median and Mode

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