Question

If the mean of a frequency distribution is 7.5 and if xi = 120 + 3k, Zf = 30, then k is equal to:

a) 40
b) 35
c) 50
d) 45

Answer 1

The answer of the given equation that "If the mean of a frequency distribution is 7.5 and if xi = 120 + 3k, Zf = 30, then k is equal to" is b) 35.

Step-by-step explanation:

The mean
`(\(\bar{x}\))` of a frequency distribution can be calculated using the formula:

`\[ \bar{x} = (\sum (x_i \cdot f_i))/(\sum f_i) \]`

Given that
`\(x_i = 120 + 3k\)` and
`\(Zf = 30\)`, we have:

`\[ 7.5 = (\sum ((120 + 3k) \cdot 30))/(\sum 30) \]`

Solving for
`\(\sum ((120 + 3k) \cdot 30)\)`, we get:

`\[ \sum ((120 + 3k) \cdot 30) = 7.5 * \sum 30 \]`

`\[ \sum ((120 + 3k) \cdot 30) = 7.5 * 30 * 30 \]`

`\[ \sum ((120 + 3k) \cdot 30) = 6750 \]`

Now, substitute
`\(Zf = 30\)` and solve for \(120 + 3k\):

`\[ 6750 = 30 * (120 + 3k) \]`

`\[ 225 = 120 + 3k \]`

`\[ 3k = 105 \]`

`\[ k = 35 \]`

Therefore, the value of
`\(k\)` is b)35.