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The table below shows groups of children in a class according to their heights:

Height (cm) Number of children
135-140 5
140-145 8
145 – 150 10
150-155 9
155-160 6
160-165 3

 a. If the children are lined up according to their heights, the median is the height of the child in which position?

b. According to the table, the height of this child is between what limits?

c. What are the assumptions used to compute the median?

d. What is the median height according to these assumptions?

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Height (cm) Number of children
Below 140 5
Below 145 13
Below 150 23
Below 155 32
Below 160 38
Below 165 41

a. Height of the 21st child is the median height. 

b. Height of the 21st child is between 145 cm and 150 cm. 

c. Methods to find the median are. 

1. Divide 5 cm in between 145 cm and 150 cm into 10 equal sections. 

2. Consider that the height of each subgroup is exactly on the midpoint of the subgroup.

Height of the 14th child is in between 145 cm and 145\(\cfrac{5}{10}\) cm.

Similarly, the height of the 15th student is in between  145\(\cfrac{5}{10}\) cm and

145\(\cfrac{5}{10}\)cm.

i.e., 145\(\cfrac{5}{20}\)cm.

Hence height of each child can be increased by 5/10 cm.

There are 7 children to reach the 21st child from 14th child.

There are 7 children to reach the 21st child from 14th child.

i.e., 14th term is 145\(\cfrac{5}{20}\) and common difference is 5/10

Mean is the 21st term of the arithmetic sequence.

Arithmetic mean is the sum divided by the number of terms.

Mean = \(\cfrac{Sum\,of\,terms}{Number\,of\,terms}\)

When the numbers are arranged in a ascending order, then the middle term is the median.

i.e., half of the total frequency will give the median.

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