Statistics
Mean Deviation
Grade 11
Question:
<p>Runs scored by a batsman in 10 innings are: 38, 70, 48, 34, 42, 55, 63, 46, 54, 44. The mean deviation is</p>
<p>8.6</p>
<p>6.4</p>
<p>10.6</p>
<p>9.6</p>
Step-by-Step Solution
Key Concept: Mean deviation is calculated as the average of absolute deviations from the mean. First find the mean, then sum |xi - mean| for all values, and divide by n.
<p><strong>Step 1:</strong> Calculate the mean of the 10 values.</p><p>Mean = (38 + 70 + 48 + 34 + 42 + 55 + 63 + 46 + 54 + 44) ÷ 10 = 494 ÷ 10 = 49.4</p><p><strong>Step 2:</strong> Find absolute deviations from the mean for each value.</p><p>|38 - 49.4| = 11.4, |70 - 49.4| = 20.6, |48 - 49.4| = 1.4, |34 - 49.4| = 15.4, |42 - 49.4| = 7.4</p><p>|55 - 49.4| = 5.6, |63 - 49.4| = 13.6, |46 - 49.4| = 3.4, |54 - 49.4| = 4.6, |44 - 49.4| = 5.4</p><p><strong>Step 3:</strong> Sum all absolute deviations.</p><p>Sum = 11.4 + 20.6 + 1.4 + 15.4 + 7.4 + 5.6 + 13.6 + 3.4 + 4.6 + 5.4 = 88.8</p><p><strong>Step 4:</strong> Divide by number of observations (n = 10).</p><p>Mean Deviation = 88.8 ÷ 10 = 8.88</p><p>∴ Answer: A</p>
Correct Answer: A