Question

3.) wrize the formula to find median a grouped data​

Answer 1

Answer:

The formula for median in a grouped data is median=l+(n2−cff)×h, where l represent the lower limit of the median class, n represents the total sum of all frequencies, cf represent the cumulative frequency before the median class, f represent the frequency of the median class and h represents the class width.

Step-by-step explanation:

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Answer 2

Step 1. Firstly we have to make a table with 3 columns.

• First column is made for the class interval
• Second column is made for the frequency
• Third column is made for the cumulative frequency.

Step 2. Now we have to write the class intervals and frequency in the respective columns.

Step 3. Now let us write the cumulative frequency in the column.

Step 4. Now we have to find the sum of frequencies (∑f)

Step 5. Now we have to find n/2, find the class whose cumulative frequency is greater than and nearest to n/2 that's median.

Step 6. Now we use the formula that is given below:

${\small{\underline{\boxed{\sf{\rightarrow \quad l \: = \Bigg(\dfrac{\dfrac{n}{2}-cf}{f} \Bigg) \times h \quad}}}}}$

A well solved example:

$\begin{gathered}\boxed{\begin{array}{|c|c|c|} \sf \: \: Height \: (In \: cm)& \: \sf \: No. \: of \: Pupil & \sf \: C.f. \\ \\90 - 100 & 5 & 5 \\100 - 110 & 2 & 7\\110 - 120 & 3 & 10\\120 - 130 & 8 & 18\\130 - 140 & 8 & 26\\140 - 150 & 6 & 32\\&\sf \:\sum\limits f=32&\ \ \\ \end{array}}\end{gathered}$

@BrainlyButterfliee

Additional information:

How to find median?

Procedure: To find median firstly we have to make the terms in ascending or descending order as we want. Then we have to check the middle term there. Then we get our answer means middle terms in that sequence is the median but if there is no middle term coming means for example there are total 6 terms then it obvious that in middle no term will come because it be even then we have to add two middle terms then we have to divide it by two. Ascending order? Small number to big number. And we get our final result!

If n is odd term then median is given by,

${\small{\underline{\boxed{\sf{\rightarrow \quad \Bigg(\dfrac{n+1}{2} \Bigg)^{th}\quad}}}}}$

If n is even term then median is given by the mean of the value of

${\small{\underline{\boxed{\sf{\quad \Bigg(\dfrac{n}{2} \Bigg)^{th} \: and \:\Bigg(\dfrac{n+1}{2} \Bigg)^{th}\quad}}}}}$

How to find mean?

Procedure: To find the mean of any term we have to add all the given digits firstly then when the sum came then we have to divide it by the total number of already given terms. And then at last we get our final result as mean. Formula to find mean is given below, we have to use it too.

${\small{\underline{\boxed{\sf{\rightarrow \dfrac{Sum \: of \: terms \: or \: observations}{Total \: number \: of \: terms \: or \: observations}}}}}}$

How to find mode?

Procedure: To find mode we have to check that which number came more time in the observation.

How to find range?

Procedure: To find range we just have to subtract the highest value and the lowest value in the observation.