Answer
Verified
324k+ views
Hint: Median of a grouped data is given by \[median = l + \left( {\dfrac{{\dfrac{n}{2} - cf}}{f}} \right) \times h\]. This formula of median for grouped data is similar to the formula of mode in an interval. Here, \[l\] represent the lower limit of the median class, \[n\] represents the total sum of all frequencies, \[cf\] represent the cumulative frequency before the median class, \[f\] represent the frequency of the median class and \[h\] represents the class width.
Complete step-by-step answer:
The formula for median in a grouped data is \[median = l + \left( {\dfrac{{\dfrac{n}{2} - cf}}{f}} \right) \times h\], where \[l\] represent the lower limit of the median class, \[n\] represents the total sum of all frequencies, \[cf\] represent the cumulative frequency before the median class, \[f\] represent the frequency of the median class and \[h\] represents the class width.
Median of a data set represents the middle value, when the data is arranged in ascending order. It generally helps in determining the most likely value of the data set, but only if the distribution of data is continuous. The value of the median should have the highest frequency for a symmetrical distribution of data. However, if the distribution of the data is unsymmetrical or skewed, median doesn’t represent the most likely value as there will be an extremely high or an extremely low value as compared to the rest of data.
Note: The median of a given set of discrete data can be found out by simply arranging it into ascending order and then picking out the middle value. However for a grouped data, we have to use the formula of median used above. It is best for a student to be well versed with these formulae.
Complete step-by-step answer:
The formula for median in a grouped data is \[median = l + \left( {\dfrac{{\dfrac{n}{2} - cf}}{f}} \right) \times h\], where \[l\] represent the lower limit of the median class, \[n\] represents the total sum of all frequencies, \[cf\] represent the cumulative frequency before the median class, \[f\] represent the frequency of the median class and \[h\] represents the class width.
Median of a data set represents the middle value, when the data is arranged in ascending order. It generally helps in determining the most likely value of the data set, but only if the distribution of data is continuous. The value of the median should have the highest frequency for a symmetrical distribution of data. However, if the distribution of the data is unsymmetrical or skewed, median doesn’t represent the most likely value as there will be an extremely high or an extremely low value as compared to the rest of data.
Note: The median of a given set of discrete data can be found out by simply arranging it into ascending order and then picking out the middle value. However for a grouped data, we have to use the formula of median used above. It is best for a student to be well versed with these formulae.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE