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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.

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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.  

  Is there an error in this question or solution?
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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
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