The number of students absent in a school was recorded every day for $147$ days and the raw data was presented in the form of the following frequency table.
No. of students absent: 5 6 7 8 9 10 11 12 13 15 18 20
No. of days: 1 5 11 14 16 13 10 70 4 1 1 1
Obtain the median and describe what information it conveys.

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Solution

Calculation of median
$x_{i}$ $f_{i}$ $c f$
5 1 1
6 5 6
7 11 17
8 14 31
9 16 47
10 13 60
11 10 70
12 70 140
13 4 144
15 1 145
18 1 146
20 1 147
$\sum f_{i} = 147$
We have,
$\Rightarrow N = 147 \Rightarrow \frac{N}{2} = \frac{147}{2} = 73.5$
The cumulative frequency just greater than $N / 2$ is $140$ and the corresponding value of the variable x is $12$ .
Hence, median = $12$ . This means that for about half the number of days, more than $12$ students were absent.

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No. of students absent:	5	6	7	8	9	10	11	12	13	15	18	20
No. of days:	1	5	11	14	16	13	10	70	4	1	1	1

$x_{i}$	$f_{i}$	$c f$
5	1	1
6	5	6
7	11	17
8	14	31
9	16	47
10	13	60
11	10	70
12	70	140
13	4	144
15	1	145
18	1	146
20	1	147
	$\sum f_{i} = 147$

The number of students absent in a school was recorded every day for 147days and the raw data was presented in the form of the following frequency table.No. of students absent:5678910111213151820No. of days:151114161310704111Obtain the median and describe what information it conveys.