Question

Find the missing value of "p" from the following table when Arithmetic Mean is 3.55.

X	1	2	3	4	5	6
F	8	9	p	16	9	8

• A. 10
• B. 9
• C. 16
• D. 8

Answer 1

The Correct Option is A

To solve the problem, we need to find the missing value of \( p \) from a frequency distribution table, given that the arithmetic mean is \( 3.55 \).

1. Understanding the Formula for Arithmetic Mean:
The formula for the mean of a frequency distribution is:

\( \bar{X} = \frac{\sum{f x}}{\sum{f}} \)
where \( f \) is frequency and \( x \) is the corresponding value.

2. Using the Given Table:

Let’s organize the values:

\( x = [1, 2, 3, 4, 5, 6] \)

\( f = [8, 9, p, 16, 9, 8] \)

3. Compute \( \sum f \) and \( \sum fx \):

First, compute known values of \( fx \):

\( 1 \times 8 = 8 \)

\( 2 \times 9 = 18 \)

\( 3 \times p = 3p \)

\( 4 \times 16 = 64 \)

\( 5 \times 9 = 45 \)

\( 6 \times 8 = 48 \)

So,
\( \sum fx = 8 + 18 + 3p + 64 + 45 + 48 = 183 + 3p \)

\( \sum f = 8 + 9 + p + 16 + 9 + 8 = 50 + p \)

4. Substituting into the Mean Formula:

Given \( \bar{X} = 3.55 \), so:

\( \frac{183 + 3p}{50 + p} = 3.55 \)

5. Solving the Equation:

Cross-multiplying:

\( 183 + 3p = 3.55 (50 + p) \)

\( 183 + 3p = 177.5 + 3.55p \)

Subtract \( 177.5 \) from both sides:

\( 5.5 + 3p = 3.55p \)

Subtract \( 3p \) from both sides:

\( 5.5 = 0.55p \)

Divide both sides by 0.55:

\( p = \frac{5.5}{0.55} = 10 \)

Final Answer:
The missing value \( p \) is \({10} \).