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.