Question

The following distribution represents the height of 160 students of a school.

Height (in cm)	No. of Students
140 – 145	12
145 – 150	20
150 – 155	30
155 – 160	38
160 – 165	24
165 – 170	16
170 – 175	12
175 – 180	8

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

1. The median height.
2. The interquartile range.
3. The number of students whose height is above 172 cm.

Answer 1

Height (in cm)	No. of students	Cumulative frequency
140 – 145	12	12
145 – 150	20	32
150 – 155	30	62
155 – 160	38	100
160 – 165	24	124
165 – 170	16	140
170 – 175	12	152
175 – 180	8	160
	N = 160

Taking height of student along x-axis and cumulative frequency along y-axis we will draw an ogive.

i. ∴ Median = `160/2` = 80^th term

Through mark for 80, draw a parallel line to x-axis which meets the curve; then from the curve draw a vertical line which meets the x-axis at the mark of 157.5.

ii. Since, number of terms = 160

Lower quartile (Q₁) = `(160/4)` = 40^th term = 152

Upper quartile (Q₃) = `((3 xx 160)/4)` = 120^th term = 164

Inner Quartile range = Q₃ – Q₁

= 164 – 152

= 12

iii. Through mark for 172 on x-axis, draw a vertical line which meets the curve; then from the curve draw a horizontal line which meets the y-axis at the mark of 145.

The number of students whose height is above 172 cm = 160 – 144 = 16