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In statistics, for grouped data, when calculating the median based on formula $Median = L_m + \left [ \frac { \frac{n}{2} - F_{m-1} }{f_m} \right ] \times c$

where $c$ is the size of the median class
$F_{m-1}$ is the cumulative frequency of the class before median class
$f_m$ is the frequency of the median class
$n$ is the total number of the data

I noticed some resources mentioned $L_m$ as lower class limit, but some lower class boundary. Which one is correct?

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1 Answers 1

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After some consideration, in my opinion, "lower boundary" will make more sense rather than lower limit. For example, this is the data,

 Class  Frequency  1       1  2       1  3       1  4       1 

Based on the data, using we can know that the median is 2.5, without calculation. If using the formula as mentioned above, $\frac{n}{2}$ will get 2, there for the class contains the median is class 2, then using $L_m$ is a lower boundary,

$median = 1.5 + \left[ \frac{2 -1}{1}\right] \times 1 = 2.5$

This doesn't make sense for using lower limit. If changing the class to

 Class Frequency  1-2    1  3-4    1  5-6    1  7-8    1 

Using the method above, we will get,

$median = 2.5 + \left[ \frac{2 -1}{1}\right] \times 2 = 4.5$

However, if using class limit, then we will get 5.