The weights in gm of a sample of 100 potatoes.

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Use graph paper for this question.
The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 21 Measures of Central Tendency Ex 21.6 Q3.1
(i) Calculate the cumulative frequencies.
(ii) Draw the cumulative frequency curve and from it determine the median weight of the potatoes. (1996)

Solution:

Representing the given data in cumulative frequency table :

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 21 Measures of Central Tendency Ex 21.6 Q3.2

Now plot the points (60, 8), (70, 18), (80, 30), (90, 46), (100, 64),
(110, 78), (120, 90), (130, 100) on the graph and join them
in a free hand to form an ogive as shown

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 21 Measures of Central Tendency Ex 21.6 Q3.3

Here n =100 which is even.
Median = \frac { 1 }{ 2 } \left[ \frac { n }{ 2 } th\quad term+\left( \frac { n }{ 2 } +1 \right) th\quad term \right]
= \frac { 1 }{ 2 } \left[ \frac { 100 }{ 2 } +\left( \frac { 100 }{ 2 } +1 \right) th\quad term \right]
= \frac { 1 }{ 2 } \left[ 50th\quad term+51th\quad term \right]
= 50.5
Now take a point A (50.5) on they-axis and from A
draw a line parallel to x-axis meeting the curve at R
From P, draw a perpendicular on x-axis meeting it at Q.
Q is the median which is = 93 gm.

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