<p>The following data gives the distribution of height of students:</p><table border='1'><tr><th>Height (in cm)</th><td>160</td><td>150</td><td>152</td><td>161</td><td>156</td><td>154</td><td>155</td></tr><tr><th>Number of students</th><td>12</td><td>8</td><td>4</td><td>4</td><td>3</td><td>3</td><td>7</td></tr></table><p>The median of the distribution is</p>
Step-by-Step Solution
Key Concept: Arrange data in ascending order and find the middle value using the position formula (n+1)/2 for odd n, or average of two middle values for even n. The cumulative frequency helps locate the median class.
<p><strong>Step 1:</strong> Arrange the heights in ascending order and their frequencies:</p><p>Height (cm): 150, 152, 154, 155, 156, 160, 161</p><p>Frequency (f): 2, 8, 4, 4, 3, 1, 3</p><p><strong>Step 2:</strong> Calculate cumulative frequency:</p><p>CF: 2, 10, 14, 18, 21, 22, 25</p><p><strong>Step 3:</strong> Total number of students n = 2+8+4+4+3+1+3 = 25 (odd)</p><p><strong>Step 4:</strong> Median position = (n+1)/2 = (25+1)/2 = 13th term</p><p><strong>Step 5:</strong> From cumulative frequency, the 13th term lies in the class where CF ≥ 13. At height 154 cm, CF = 14, so the 13th observation is 154 cm.</p><p>∴ Median = <strong>154 cm</strong></p>
Correct Answer: B