Question

Use Graph paper for this question.

A survey regarding height (in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded:

Height in cm	135 – 140	140 – 145	145 – 150	150 – 155	155 – 160	160 – 165	165 – 170
No. of boys	4	8	20	14	7	6	1

Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other axis draw an ogive of the above distribution. Use the graph to estimate the following:

1. the median
2. lower quartile
3. if above 158 cm is considered as the tall boys of the class. Find the number of boys in the class who are tall.

Answer 1

Height in cm	No. of Boys	c.f.
135 – 140	4	4
140 – 145	8	12
145 – 150	20	32
150 – 155	14	46
155 – 160	7	53
160 – 165	6	59
165 – 170	1	60
	n = 60

i. Median = `n/2`th observation

= `60/2`th observation

= 30th observation

= 150 cm (From ogive)

ii. Lower quartile = `n/4`th observation

= `60/4`th observation

= 15th observation

= 146 cm (From ogive)

iii. No. of boys whose height is less than 158 cm = 51. (From ogive)

∴ No. of tall boys = 60 – 51 = 9.