Question

students marks (x) d = x - a (a=50) a 85 +35 b 60 +10 c 50 (a) 0 d 75 +25 e 55 +5 f 40 -10 g 55 +5 h 70 +20 i 45 -5 j 65 +15

Explanation:

To find the mean of the marks using the assumed mean method, we follow these steps:

Step 1: Identify the number of students (\(n\))

There are 10 students (A to J), so \(n = 10\).

Step 2: Calculate the sum of deviations (\(\sum d\))

We add up all the values in the \(d = X - A\) column:
\[

$$\begin{align*} \sum d&= 35 + 10 + 0 + 25 + 5 - 10 + 5 + 20 - 5 + 15\\ &= (35 + 10 + 25 + 5 + 5 + 20 + 15) + (0 - 10 - 5)\\ &= (115) + (-15)\\ &= 100 \end{align*}$$

\]

Step 3: Use the formula for the mean (\(\bar{X}\)) using the assumed mean method

The formula is:
\[
\bar{X} = A + \frac{\sum d}{n}
\]
where \(A = 50\) (the assumed mean), \(\sum d = 100\), and \(n = 10\).

Substitute the values into the formula:
\[
\bar{X} = 50 + \frac{100}{10}
\]
\[
\bar{X} = 50 + 10
\]
\[
\bar{X} = 60
\]

Answer:

The mean of the marks is \(\boxed{60}\).