A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:


Height in cm



Number of Girls



Less than 140



4



Less than 145



11



Less than 150



29



Less than 155



40



Less than 160



46



Less than 165



51



Find the median height.

To calculate the median height we need to find the class interval and their corresponding frequencies.

The given distribution being of the less than type 140, 145, 150,….165 give the upper limit of the corresponding class intervals. So, the classes should be below 140, 140-145, 145-150,….160-165. Observe that from the given distribution, we find that there are 4 girls with height less than 145 and 4 girls with height less than 140. Therefore, the number of girls with height in the interval 140-145 is 11 – 4 = 7


Similarly, the frequency of 145-150 is 29 – 11 = 19, for 150-155 it is 40 – 29 = 11 and so on so our frequency distribution table with the given cumulative frequency becomes:


Class interval



Frequencies



Cumulative frequency



Below 140



4



4



140-145



7



11



145-150



18



29



150-155



11



40



155-160



6



46



160-165



5



51



Now N = 51


So, = = 25.5


This observation lies in the class 145 – 150


Then, l (lower limit) = 145


f = 11 and h = 5


Median = 145 + * 5


= 145 + 4.03


= 149.03


So, the median height of the girls is 149.03 cm. This means that the height of the about 50% of the girls is less than this height and 50% are taller than this height.


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