Question

Find the median of the following data:

Height (in cm)	Less than 120	Less than 140	Less than 160	Less than 180	Less that 200
Number of students	12	26	34	40	50

Answer 1

Given:

To calculate the median height, we need to convert the given data into the continuous grouped frequency distribution.

Height	Number of students	cf
below 120	12	12
120-140	26 - 12 = 14	26
140-160	34 - 26 = 8	34
160-180	40 - 34 = 6	40
180-200	50 - 40 = 10	50

Here, n = 50

So, \(\frac n2 = 25\)

Since, the cumulative frequency just greater than 25 is 26 and the corresponding class interval is 120-140

Median class = 120-140

Now,

l = 120

f = 14

cf = 12

h = 20

Median = \(l + \left(\frac{\frac n2 - cf}{f}\right) \times h\)

\(= 120 + \left(\frac{25 -12}{14}\right) \times 20\)

\(= 120 + 18.57\)

\(= 138.57\) cm

Hence, the median height of students is 138.57 cm.

Answer 2

Therefore, Median = 138.57

Comments

The frequency asked in the question is different. This answer is a pure blunder!

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We are converting less than frequency table into normal frequency table. Given frequency for less than table is commutative frequency, we have to find frequencies for corresponding classes with the help of cumulative frequencies.