Question
Download Solution PDFWhat is the mean deviation of first 10 even natural numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Mean deviation = \(\frac{1}{n}|x_i-\bar{X}|\)
Where,
\(\bar{X}= \frac{∑ x}{n}\) = mean,
∑x = sum of all observations,
n = number of observations.
Calculation:
First 10 even natural numbers are
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Mean,
X̅ = \(\rm \frac{2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20}{10}\)
⇒ X̅ = 11
Therefore, the mean value is 11
Now, subtract each mean from the first 10 even natural numbers, and ignore the minus symbol if any
⇒ Mean deviation = \(\frac{1}{n}|x_i-\bar{X}|\)
⇒ Mean deviation \(=\frac{1}{10}(|2 - 11|+ |4 - 11| + |6-11|+|8-11|+|10-11|+\\|12-11|+|14-11|+|16-11|+|18-11|+|20-11|\)
⇒ \(\rm\frac{9 + 7 + 5 + 3 + 1 + 1 + 3 + 5 + 7 + 9}{10}\) = \(\frac{50}{10}\)
∴ The mean deviation of the first 10 even natural numbers is 5.
Last updated on May 30, 2025
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