# The Following Distribution Represents the Height of 160 Students of a School. 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 - Mathematics

Sum

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.

#### Solution

 Height (in cm) Number of students (f) Cumulative Frequency(c.f) 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 scale as 2 cm=5 cm on an x-axis and 2 cm = 20 students on the y-axis, the Ogive is drawn as below:

1) Median Height = (N/2)^"th" value = (160/2)^"th" value  = 80 th value  = 157 cm (Approx)

2) Lower Quartile, Q_1 = (N/4)^"th" value  = (160/4)^"th" value = 40 th value 152 cm

Upper quartile, Q_3 = ("3N"/4)^"th" value = ((3xx160)/4)^"th" value = 120^"th"  value = 164 cm

Inter Quartile Range,  Q_3  - Q_1 = 164 - 152 = 12 cm

3) The number of students whose height is more than 172 cm = 160 – 142 = 18 students.

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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 24 Measure of Central Tendency(Mean, Median, Quartiles and Mode)
Exercise 24 (E) | Q 1 | Page 375