A survey regarding the heights in (cm) of 51 girls of class X of a sch

A survey regarding the heights in (cm) of 51 girls of class X of a school was conducted and the following data was obtained. Find the median height and the mean using the formulae.Height (in cm)Number of GirlsLess than 1404Less than 14511Less than 15029Less than 15540Less than 16046Less than 16551

Answer»

N = 51

⇒ \(\frac{N}{2}\) = \(\frac{51}{2}\) = 25.5

As 29 is just greater than 25.5, therefore median class is 145-150.

Median = I + \(\frac{(\frac{N}{2}-C)}{f}\) X h

Here, l = lower limit of median class = 145

C = C.F. of the class preceding the median class = 11

h = higher limit - lower limit = 150 − 145 = 5

f = frequency of median class = 18

∴ median = 145 + \(\frac{(25.5-11)}{18}\) X 5

=149.03

Mean by direct method

Mean = \(\frac{∑fx}{N}\)

= \(\frac{7637.5}{51}\)

= 149.75