Question

If the survey data (in cm) of height of 50 girls of class X in a school are as follows:

Length (in cm)	Number of girls
Less than 140 cm	4
Less than 145 cm	11
Less than 150 cm	29
Less than 155 cm	40
Less than 160 cm	46
Less than 165 cm	50

 उनकी ऊँचाइयों की माध्यिका ज्ञात करें -

1. 144.03 cm
2. 148.89 cm
3. 145.03 cm
4. 149.03 cm

Answer 1

Correct Answer - Option 2 : 148.89 cm

Height (in cm)	f	C.F.
below 140	4	4
140-145	7	11
145-150	18	29
150-155	11	40
155-160	6	46
160-165	4	50

 

Concept used:

Median = I +  (N/2 − C)/f  × h

Here, l = lower limit of the median class

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

h = higher limit - lower limit

f = frequency of median class

Calculation:

N = 50

⇒ N/2 = 50/2 = 25

As 29 is just greater than 25, therefore the median class is 145 - 150. 

The lower limit of median class = 145 

C = 11 

h = 150 − 145 = 5 

f = 18 

Median = [145 + (25 − 11)/18]5

⇒ 145 + 3.89

⇒ 148.89

∴ Median is 148.89