Calculation of Mean, Median, and Mode in Special Cases
In some cases, the calculation of Mean, Median, and Mode is different. Following are some of the treatment of special cases.
|
Cases |
Mean |
Median |
Mode |
|---|---|---|---|
|
Cumulative Series (‘Less than’ or ‘More than’) |
Convert the cumulative frequency to a basic frequency distribution before calculating the mean as usual. |
Convert the cumulative frequency to a basic frequency distribution before calculating the median as usual. |
Calculate mode as usual after converting the cumulative frequency into a basic frequency distribution. |
|
Mid-Values are given |
Calculate the mean in the usual way. There is no need to transform mid-values into class intervals. |
Calculate the median after converting the mid-values to class intervals. |
Calculate the mode after converting the mid-values into class intervals. |
|
Inclusive Class-interval |
Compute the mean as usual. The series should not be changed into an exclusive class-interval series. |
To determine the median, the class interval is transformed into an exclusive class-interval series. |
After converting class intervals into exclusive class interval series, the mode is determined. |
|
Open-End Series
|
In order to calculate the mean, missing class limits will be assumed, and this depends on the distribution of class intervals among other classes. |
The median is calculated using the normal procedure without completing the class intervals.
|
Mode is computed as usual, without completing the class intervals. |
|
Unequal Class-intervals |
In this case, after calculating the mid-values for each interval, the mean may be calculated as usual. There is no need to make equal class-intervals. |
The median can be determined in the usual manner regardless of unequal class intervals. |
Class intervals and frequencies need to be adjusted in order to calculate mode. |
Mean, Median and Mode| Comparison, Relationship and Calculation
A single value used to symbolise a whole set of data is called the Measure of Central Tendency. In comparison to other values, it is a typical value to which the majority of observations are closer. Average and Measure of Location are other names for the Measure of Central Tendency. In statistical analysis, the three principal measurements used in central tendency are Arithmetic Mean, Median, and Mode.
What is Mean?
Arithmetic Mean is one approach to measure central tendency in statistics. This measure of central tendency involves the condensation of a huge amount of data to a single value.
What is Median?
The positional value of a variable known as the median distributes the distribution into two parts that are equal; i.e., values above or equal to the median value are included in the first part, while all values below or equal to the median are included in the second part.
What is Mode?
Mode refers to the variable that occurs most of the time in the given series. In simple words, mode is a variable that repeats itself most frequently in a given series of variables (say, X). Mode is denoted as ‘Z‘.
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