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

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(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 +

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$20$

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(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 $0.2$: $p = \frac{4}{0.2} = 20$.

Class interval	Frequency
$150-153$	$7$
$154-157$	$7$
$158-161$	$15$
$162-165$	$10$
$166-169$	$5$
$170-173$	$6$

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$5$	$7$	$12$	$9$	$13$	$5$

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

Convert the given frequency distribution into a continuous grouped frequency distribution:

Class interval Frequency

$150-153$ $7$

$154-157$ $7$

$158-161$ $15$

$162-165$ $10$

$166-169$ $5$

$170-173$ $6$

In which intervals would $153.5$ and $157.5$ be included?

If the information gathered by an investigator is from an already existing source of data,then such information is called .........

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.

Draw a histogram for the data given below:

Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$ $50-60$

Frequency $5$ $7$ $12$ $9$ $13$ $5$

Find the median of the observations $18, 8, 12, 3, 20, 4, 10, 5$.

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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}$