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:

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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 \(\boxed{60}\).