<p>The mean deviation about the mean of the following distribution is</p><table border='1'><tr><th>Size (x<sub>i</sub>)</th><td>20</td><td>21</td><td>22</td><td>23</td><td>24</td></tr><tr><th>Frequency (f<sub>i</sub>)</th><td>6</td><td>4</td><td>5</td><td>1</td><td>4</td></tr></table>
Step-by-Step Solution
Key Concept: Mean deviation about mean = Σfi|xi - x̄|/Σfi. First calculate the mean x̄ using Σfixi/Σfi, then find absolute deviations from this mean, weight them by frequencies, and divide by total frequency.
<p><strong>Step 1:</strong> Calculate total frequency and sum of fixi</p><p>Σfi = 6 + 4 + 5 + 1 + 4 = 20</p><p>Σfixi = 6(20) + 4(21) + 5(22) + 1(23) + 4(24) = 120 + 84 + 110 + 23 + 96 = 433</p><p><strong>Step 2:</strong> Calculate mean</p><p>x̄ = Σfixi/Σfi = 433/20 = 21.65</p><p><strong>Step 3:</strong> Calculate |xi - x̄| for each class</p><p>|20 - 21.65| = 1.65, |21 - 21.65| = 0.65, |22 - 21.65| = 0.35, |23 - 21.65| = 1.35, |24 - 21.65| = 2.35</p><p><strong>Step 4:</strong> Calculate Σfi|xi - x̄|</p><p>Σfi|xi - x̄| = 6(1.65) + 4(0.65) + 5(0.35) + 1(1.35) + 4(2.35) = 9.9 + 2.6 + 1.75 + 1.35 + 9.4 = 25</p><p><strong>Step 5:</strong> Calculate mean deviation</p><p>MD = Σfi|xi - x̄|/Σfi = 25/20 = 1.25</p><p>∴ Answer: B (1.25)</p>
Correct Answer: B