Statistics
Mean Deviation
Grade 11
Question:
<p>When tested, the lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623. The mean deviation (in hours) from their mean is</p>
<p>178</p>
<p>179</p>
<p>220</p>
<p>356</p>
Step-by-Step Solution
Key Concept: Mean deviation measures average absolute distance of all observations from their mean. Calculate mean first, then find sum of |xᵢ - mean|, divide by number of observations.
<p><strong>Step 1: Calculate the mean</strong></p><p>Mean = (1357 + 1090 + 1666 + 1494 + 1623)/5 = 7230/5 = 1446 hours</p><p><strong>Step 2: Calculate deviations from mean (absolute values)</strong></p><p>|1357 - 1446| = 89</p><p>|1090 - 1446| = 356</p><p>|1666 - 1446| = 220</p><p>|1494 - 1446| = 48</p><p>|1623 - 1446| = 177</p><p><strong>Step 3: Sum of absolute deviations</strong></p><p>Sum = 89 + 356 + 220 + 48 + 177 = 890</p><p><strong>Step 4: Calculate mean deviation</strong></p><p>Mean Deviation = 890/5 = 178 hours</p><p><strong>∴ Answer: A (178 hours)</strong></p>
Correct Answer: A