JAMIA 2022 — Mathematics PYQ

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Question

JAMIA 2022 — Mathematics PYQ

JAMIA | Mathematics | 2022

Marks obtained by 4 students are : 25, 35, 45, 55. The average deviation from the mean is

Choose the correct answer:

Explanation

Step 1: Calculate the Mean ( $\bar{x}$ )

The mean is the sum of all observations divided by the total number of observations ( $n = 4$ ):

\bar{x} = \frac{25 + 35 + 45 + 55}{4}

\bar{x} = \frac{160}{4} = 40

Step 2: Calculate the Absolute Deviations from the Mean

We find the distance of each mark from the mean ( $40$ ) by taking the absolute value $|x_i - \bar{x}|$ :

For $25$ : $|25 - 40| = |-15| = 15$
For $35$ : $|35 - 40| = |-5| = 5$
For $45$ : $|45 - 40| = |5| = 5$
For $55$ : $|55 - 40| = |15| = 15$

Step 3: Calculate the Average Deviation ( $MD$ )

The average deviation is the sum of these absolute deviations divided by the number of students:

MD = \frac{\sum |x_i - \bar{x}|}{n}

MD = \frac{15 + 5 + 5 + 15}{4}

MD = \frac{40}{4}

MD = 10

Final Answer

The average deviation from the mean is $10$ .