Question

Given data consists of distinct values of $𝑥_𝑖$ occurring with frequencies $𝑓_𝑖.$ The mean value for the data is _____. (rounded off to one decimal place)

$X_i$	5	6	8	10
$F_i$	8	10	10	12

Answer 1

Correct Answer: 7.5

To find the mean of the given data, we'll use the formula for the mean in a frequency distribution: 
\[ \text{Mean} = \frac{\sum (X_i \cdot F_i)}{\sum F_i} \] 
We perform the following calculations:

• Calculate \( X_i \cdot F_i \) for each \( X_i \).

$X_i$	5	6	8	10
$F_i$	8	10	10	12
$X_i \cdot F_i$	40	60	80	120

• Calculate the total \( \sum (X_i \cdot F_i) = 40 + 60 + 80 + 120 = 300 \).
• Calculate the total frequency \( \sum F_i = 8 + 10 + 10 + 12 = 40 \).
• Substitute these sums into the mean formula: 
  \[ \text{Mean} = \frac{300}{40} = 7.5 \]

Thus, the mean is 7.5.