<p>The following data give the distribution of heights 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 cumulative frequency method. For n observations, median is at position (n+1)/2 or between positions n/2 and (n/2)+1.
<p><strong>Step 1:</strong> Arrange heights in ascending order with their frequencies:</p><p>Height (cm): 150, 152, 154, 155, 156, 160, 161</p><p>Frequency: 2, 8, 4, 4, 3, 1, 3</p><p><strong>Step 2:</strong> Calculate cumulative frequencies:</p><p>150: 2, 152: 10, 154: 14, 155: 18, 156: 21, 160: 22, 161: 25</p><p><strong>Step 3:</strong> Total number of students n = 2+8+4+4+3+1+3 = 25</p><p><strong>Step 4:</strong> Median position = (n+1)/2 = (25+1)/2 = 13th observation</p><p><strong>Step 5:</strong> From cumulative frequency: 10th to 14th observations fall in the class with height 154 cm (cumulative frequency reaches 14 at height 154)</p><p>∴ Answer: B (Median = 154 cm)</p>
Correct Answer: B