Question

calculate the median for the following data ci 0-10 10-20 20-30 30-40 40-50 50-60 f 5 8 20 15 7 5

Answer 1

Here is the answer the median is 28.5

Hope it helps you

Answer 2

The median of the given data will be 28.5

Step-by-step explanation:

Given:

classes = 0-10  10-20  20-30  30-40 40-50  50-60

frequency= 5  8  20  15  7  5

To find:

median for the data

Solution:

For median, we take out the cumulative frequencies using the frequencies given

c.f. for the class 0-10 will be the same as the frequency=5

c.f. for the class 10-20=5+8= 13

c.f. for the class 20-30= 13+20= 33

c.f. for the class 30-40=33+15= 48

c.f. for the class 40-50 =48+7= 55

c.f. for the class 50-60 =55+5 = 60 = N

$\frac{N}{2}$= $\frac{60}{2}$ = $30$th term

The closest and greater than c.f. to 30 is 33

∴ The corresponding class 20-30 is the median class

Median= $l+\frac{\frac{N}{2} -c.f.}{f} (h)$

where $l$= lower limit of the median class = 20

$\frac{N}{2}$=30

$c.f.$= cumulative frequency of the class preceding the median class = 13

$f$= frequency of the median class=20

$h$= difference between the upper limit and lower limit of the median class

 = 30-20 = 10

Median= $l+\frac{\frac{N}{2} -c.f.}{f} (h)$

Median= $20+\frac{30 -13}{20} (10)$

Median= $20+\frac{17}{20} (10)$

Median= $20+\frac{170}{20}$

Median= $20+8.5$

∴ Median= $28.5$ units

Hence, the median of the data will be 28.5 units