Question

For the following data find median observations 10,12,14,16,18,20 frequency 1,4,5,9,1,3

Answer 1

Answer:

5

Step-by-step explanation:

Observation       Frequency     Cumulative Frequency

10                             1                                     1

12                             4                                    5

1 4                            5                                   10

16                            9                                    19

18                             1                                     20

20                            3                                    23

Total number of terms = n = 23  

Hence, 23 is an odd number so we will apply formula of median for odd number.

Median = Value of (n+1/2)th observation

             = Value of (23+1/2)th observation

            = Value of (24/2)th observation

           = Value of 12th observation

Value of 12th observation in table is 5 so,

Median = 5

Answer 2

Answer: Median: 16

Step to find Median:

Since given data is ungrouped data,so

Count the frequency,or Calculated CF for the given table


$\begin{table}[] \begin{tabular}{|l|l|l|} \cline{1-3} Observation & Freq. & \begin{tabular}[c]{@{}l@{}}Cumulative\\ Frequency\end{tabular} \\ \cline{1-3} 10 & 1 & 1 \\ \cline{1-3} 12 & 4 & 5 \\ \cline{1-3} 14 & 5 & 10 \\ \cline{1-3} 16 & 9 & 19 \\ \cline{1-3} 18 & 1 & 20 \\ \cline{1-3} 20 & 3 & 23 \\ \cline{1-3} \end{tabular} \end{table}$

It is clear from the last entry of CF that total frequencies are 23
I.e.

n = 23

As we read that if total observations are odd than median is
${( \frac{n + 1}{2} })^{th} \: \: term$


So here

$\frac{23 + 1}{2} \\ \\ = 12 \: term \: is \: median$


Now from the table look for 12th term ,as 11-19 all terms are 16, so 12 term is also 16.

So, median is 16.

Hope it helps you.