Question

how to find the 1st and 2nd quartile and the median from a histogram?

Answer 1

Histogram gives only the mode directly. ie the mid point of the highest bar gives the mode.. How ever median calculation is possible from histogram.. using the formula

First we need to identify median bar For that find the cumulative frequency for each bar. Then calculate N/2 where N is the total number of observations or the sum of the height of all bars. The bar with immediate cumulative frequency greater than N/2 will be the median bar.

L: Lower limit of the median bar : c is the cumulative frequency preceeding the median bar; f: is the height of the median bar; h: width of the median bar.

Another way to calculate median from the graphical mode and mean of the data is using the formula

Mean can be calculated by considering the midpoint of the bars and multiplying them with the height of the respective bars and dividing with the total height of all the bars..

First quartile can also be obtained with the help of the formula . For that first locate the bar where you can find the first quartile Calculate N/4. The bar having cumulative frequency next to N/4 will be the First quartile bar..Then Use the formula

Where L₁: Lower limit of the first quartile bar : c₁ is the cumulative frequency preceeding the First quartile bar; f: is the height of the First Quartile bar; h₁: width of the First Quartile bar.

Similarly third quartile can be found using the formulaThe letter interpretations are similar to that of the first quartile formula

Hope you have asked for 3rd quartile in the question wrongly typed as 2nd quartile. 2nd Quartile and median are the same