Subjects statistics

Median Price 1Cbd43

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1. **Problem:** Based on the histogram of home prices (in thousands of dollars) for 304 homes, determine which statement must be true. 2. **Understanding the histogram:** The histogram shows the number of homes sold in price intervals from $250,000 to $2,500,000. The tallest bar is at $750,000 with about 120 homes sold. 3. **Analyzing each statement:** - (A) Minimum price is $250,000. The histogram starts at $250,000, so minimum price could be $250,000 or possibly lower, but histogram shows no homes below $250,000. So (A) could be true. - (B) Maximum price is $2,500,000. The histogram ends at $2,500,000 with zero homes sold, so maximum price is less than or equal to $2,500,000, but not necessarily equal. So (B) is not necessarily true. - (C) Median price is not greater than $750,000. Since 304 homes sold, median is the 152nd home. Counting cumulative frequencies from left to right, the cumulative count reaches 140 at $500,000 and then 260 at $750,000, so median lies in the $500,000 to $750,000 interval, so median price is not greater than $750,000. So (C) is true. - (D) Mean price is between $500,000 and $750,000. Mean depends on all data, and since there are homes priced higher than $750,000, mean could be higher. Cannot be sure from histogram alone. So (D) is not necessarily true. - (E) Upper quartile is greater than $1,500,000. Upper quartile is the 75% percentile, which is the 228th home. Cumulative frequency at $1,500,000 is about 280 homes, so upper quartile is less than or equal to $1,500,000, so (E) is false. 4. **Conclusion:** The only statement that must be true is (C). **Final answer:** (C) The median price is not greater than $750,000.