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 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 |
Height (in cm) f C.F.
below 140 4 4
140-145 7 11 1
145-150 18 29
150-155 11 40
155-160 6 46
160-165 5 51
N = 51
⇒ N/2 = 51/2 = 25.5
As 29 is just greater than 25.5, therefore median class is 145-150.
Median = 
Here, l = lower limit of median class = 145
C = C.F. of the class preceding the median class = 11 1/2
h = higher limit – lower limit = 150 – 145 = 5
f = frequency of median class =18
∴ Median = 145 + 
1/2
= 149.03
Mean by direct method
Height (in cm) f xi fxi
below 140 4 137.5 550
140-145 7 142.5 997.5
145-150 18 147.5 2655
150-155 11 152.5 1677.5
155-160 6 157.5 945
160-165 5 162.5 812.5 1
Mean = 
= 7637.5/51
= 149.75
Couldn't generate an explanation.
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