how to calculate median and mode
earlier we have covered the definition , calculation and formula for different types of means. in this post we are discussing the calculation of median and mode
Median of a set of observation is the middle most value when the observations
are arranged in order of magnitude. The number of observations smaller than
median is the same as the number of observations greater than it.
It is independent of the presence of extreme values.
Calculation of Median
For ungrouped data, the observations have to be arranged in order of
magnitude to calculate median. If the number of observations is odd, the
value all the middle most observation is the median. However, if the
number is even, the arithmetic mean of the two middle most values is taken as median.
For simple frequency distribution, to calculate median, we have to
calculate the less than type cumulative frequency distribution. If the total
frequency is N, the value of the variable corresponding to the cumulative
frequency N+1/2 gives the median.
Median of a grouped frequency distribution is that value of the variable
which corresponds to the cumulative frequency N/2. Median can be
calculated using either the formula or graph. Both these methods are given
below:
To use the formula for median we have to calculate the cumulative
frequency for each class. The class in which the cumulative frequency N/2
lies is called the median class. To compute median we apply the following
formula:
An appropriate value of median can be calculated graphically from ogives
or cumulative frequency polygon.
We have to draw a horizontal line from the point N/2 on the vertical axis, which shows the cumulative frequency, until it meets the ogives (either less than type or greater than type).
From this point of intersection, a perpendicular is dropped on the horizontal axis.
The position of the foot of the perpendicular is read from the horizontal scale showing the values of the variable.
Mode of a given set of observation is that value of the variable which occurs
with the maximum frequency.
From a simple series, mode can be calculated by locating that value which
occurs maximum number of times.
From a simple frequency distribution mode can be determined by inspection
only. It is that value of the variable which corresponds to the largest
frequency.
From the grouped frequency distribution if all classes are of equal
width, mode is usually calculated using the following formula
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Median of a set of observation is the middle most value when the observations
are arranged in order of magnitude. The number of observations smaller than
median is the same as the number of observations greater than it.
It is independent of the presence of extreme values.
Calculation of Median
For ungrouped data, the observations have to be arranged in order of
magnitude to calculate median. If the number of observations is odd, the
value all the middle most observation is the median. However, if the
number is even, the arithmetic mean of the two middle most values is taken as median.
For simple frequency distribution, to calculate median, we have to
calculate the less than type cumulative frequency distribution. If the total
frequency is N, the value of the variable corresponding to the cumulative
frequency N+1/2 gives the median.
Median of a grouped frequency distribution is that value of the variable
which corresponds to the cumulative frequency N/2. Median can be
calculated using either the formula or graph. Both these methods are given
below:
To use the formula for median we have to calculate the cumulative
frequency for each class. The class in which the cumulative frequency N/2
lies is called the median class. To compute median we apply the following
formula:
An appropriate value of median can be calculated graphically from ogives
or cumulative frequency polygon.
We have to draw a horizontal line from the point N/2 on the vertical axis, which shows the cumulative frequency, until it meets the ogives (either less than type or greater than type).
From this point of intersection, a perpendicular is dropped on the horizontal axis.
The position of the foot of the perpendicular is read from the horizontal scale showing the values of the variable.
Mode of a given set of observation is that value of the variable which occurs
with the maximum frequency.
From a simple series, mode can be calculated by locating that value which
occurs maximum number of times.
From a simple frequency distribution mode can be determined by inspection
only. It is that value of the variable which corresponds to the largest
frequency.
From the grouped frequency distribution if all classes are of equal
width, mode is usually calculated using the following formula
thank you for visiting idea tutors. you can ask your questions in the comment box. if you want to request any study material regarding these topics you can contact us via form or put the topic in the comment box
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