The mean deviation about the mean for the data xi 5 7 9 10 12 15 fi 8 6 2 2 2 6 is equal to:

The correct answer is Option 3. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Maths Q8 – JEE-MAIN 2026

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Home Maths StatisticsQuestion #428

The mean deviation about the mean for the data

\begin{array}{ccccccc} x_{i} & 5 & 7 & 9 & 10 & 12 & 15 \\ f_{i} & 8 & 6 & 2 & 2 & 2 & 6 \end{array}

is equal to:

Clue 1 of 3: Understand the concept

Mean deviation about the mean measures the average absolute difference between each data point and the mean of the data.

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Step 1: Calculate the Mean (

\bar{x}

)✦ Active

First, calculate the sum of frequencies (N) and the sum of the product of frequency and data points ( $\sum f_{i} x_{i}$ ). $\sum f_{i} = 8 + 6 + 2 + 2 + 2 + 6 = 26$ $\sum f_{i} x_{i} = (5 \times 8) + (7 \times 6) + (9 \times 2) + (10 \times 2) + (12 \times 2) + (15 \times 6)$ $= 40 + 42 + 18 + 20 + 24 + 90 = 234$ Now, calculate the mean:

\bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{234}{26} = 9

Step 2: Calculate Absolute Deviations and their Weighted Sum○ Expand

Next, calculate the absolute deviation of each data point from the mean, $| x_{i} - \bar{x} |$ , and then multiply by its corresponding frequency $f_{i}$ . Sum these products to get $\sum f_{i} | x_{i} - \bar{x} |$ . For $x_{i} = 5$ , $| 5 - 9 | = 4$ , $f_{i} | x_{i} - \bar{x} | = 8 \times 4 = 32$ For $x_{i} = 7$ , $| 7 - 9 | = 2$ , $f_{i} | x_{i} - \bar{x} | = 6 \times 2 = 12$ For $x_{i} = 9$ , $| 9 - 9 | = 0$ , $f_{i} | x_{i} - \bar{x} | = 2 \times 0 = 0$ For $x_{i} = 10$ , $| 10 - 9 | = 1$ , $f_{i} | x_{i} - \bar{x} | = 2 \times 1 = 2$ For $x_{i} = 12$ , $| 12 - 9 | = 3$ , $f_{i} | x_{i} - \bar{x} | = 2 \times 3 = 6$ For $x_{i} = 15$ , $| 15 - 9 | = 6$ , $f_{i} | x_{i} - \bar{x} | = 6 \times 6 = 36$

\sum f_{i} | x_{i} - \bar{x} | = 32 + 12 + 0 + 2 + 6 + 36 = 88

💡 Teacher's Secret Hint

Ensure all absolute deviations are positive before multiplying by frequency.

Step 3: Calculate the Mean Deviation about the Mean○ Expand

Finally, divide the sum of $f_{i} | x_{i} - \bar{x} |$ by the total frequency $\sum f_{i}$ to find the mean deviation about the mean.

M D = \frac{\sum f_{i} | x_{i} - \bar{x} |}{\sum f_{i}} = \frac{88}{26} = \frac{44}{13}

Comparing this result with the given options, we find that it matches option 3.

💡 Teacher's Secret Hint

Always simplify fractions to their lowest terms if possible.

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Maths Question 8 – JEE-MAIN 2026

Clue 1 of 3: Understand the concept

🧠 Full Solution Path