[Math] How to find quartiles using histogram

statistics

Can you suggest how can I find first and third quartiles and median after building histogram

from raw data?

I can sort the data and find the values, but still how it can be done using the chart…

Best Answer

The median $Q_2$ is the point such that the area under the bars each side of $Q_2$ is equal.

The lower quartile $Q_1$ is the point such that the area up to $Q_1$ is one quarter of the total area.

The upper quartile $Q_3$ is the point such that the area up to $Q_3$ is three quarters of the total area.

Related Solutions

[Math] Is it possible to calculate the mean and standard deviation from a median and quartiles

It's mathematically impossible to deduce mean or standard deviation from median/quartiles, because medians and quartiles discard most of the data on which the mean and standard deviation are based.

Example:

data   frequency  
   0       50      
 1.4        4     
   2       50

That has a mean of 1.0 and standard deviation of 0.9. (I'm using 2 significant figures so I don't have to go into population versus sample standard deviation.)

data     frequency    
   0       30        
 1.4       44        
   2       30

That data also has the median and quartiles the same as in your example, but now the mean is 1.2 and the standard deviation is 0.8.

data     frequency        
   0       30        
 1.4        3        
   2       70        
10000000    1

Now I've changed my maximum without changing the median or quartiles, you can see even more clearly how the median and quartiles exclude extreme data, because the mean is now 96000 and the standard deviation is 98000 (still 2 sig.fig.).

[Math] For the standard normal distribution N(0,1) , find the median, quartiles and interquartile range

Look at a table of the standard normal distribution.

At what values of z it is $\Phi(z)=0.25, \Phi(z)=0.50$ or $\Phi(z)=0.75$ ?

The values of z are the quartiles $Q_1,Q_2$ and $Q_3$.

Best Answer

Related Solutions

[Math] Is it possible to calculate the mean and standard deviation from a median and quartiles

[Math] For the standard normal distribution N(0,1) , find the median, quartiles and interquartile range

Related Question