If the mean of the following data is 20.2, fi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The formula for the mean is $\bar{x} = \frac{\sum x_i f_i}{\sum f_i}$.First,calculate the sum of frequencies $\sum f_i = 6 + 8 + p + 10 + 6 = 30 +

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(A) The formula for the mean is $\bar{x} = \frac{\sum x_i f_i}{\sum f_i}$.First,calculate the sum of frequencies $\sum f_i = 6 + 8 + p + 10 + 6 = 30 + p$.Next,calculate the sum of the products $\sum x_i f_i = (10 	imes 6) + (15 	imes 8) + (20 	imes p) + (25 	imes 10) + (30 	imes 6)$.$\sum x_i f_i = 60 + 120 + 20p + 250 + 180 = 610 + 20p$.Given the mean is $20.2$,we set up the equation: $20.2 = \frac{610 + 20p}{30 + p}$.Multiply both sides by $(30 + p)$: $20.2(30 + p) = 610 + 20p$.$606 + 20.2p = 610 + 20p$.Subtract $20p$ from both sides: $606 + 0.2p = 610$.Subtract $606$ from both sides: $0.2p = 4$.Divide by $0.2$: $p = \frac{4}{0.2} = 20$.

If the mean of the following data is $20.2,$ find the value of $p:$
$\begin{array}{|c|c|c|c|c|c|} \hline x & 10 & 15 & 20 & 25 & 30 \\ \hline f & 6 & 8 & p & 10 & 6 \\ \hline \end{array}$

Similar Questions

In a histogram, the areas of the rectangles are proportional to the frequencies. Can we say that the lengths of the rectangles are also proportional to the frequencies?

The mean of the $10$ observations is $68$. If each observation is divided by $2$ and then $6$ is added to each result, find the mean of the new observations so obtained.

Ten observations $6, 14, 15, 17, x+1, 2x-13, 30, 32, 34, 43$ are written in an ascending order. The median of the data is $24$. Find the value of $x$.

Median of the following numbers: $4, 4, 5, 7, 6, 7, 7, 12, 3$ is

Is it correct to say that in a histogram,the area of each rectangle is proportional to the class size of the corresponding class interval? If not,correct the statement.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If the mean of the following data is $20.2,$ find the value of $p:$$\begin{array}{|c|c|c|c|c|c|} \hline x & 10 & 15 & 20 & 25 & 30 \\ \hline f & 6 & 8 & p & 10 & 6 \\ \hline \end{array}$