the prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram…

the prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below. based on the histogram, which of the following statements must be true? a the minimum price is $250,000. b the maximum price is $2,500,000. c the median price is not greater than $750,000. d the mean price is between $500,000 and $750,000.

the prices, in thousands of dollars, of 304 homes recently sold in a city are summarized in the histogram below. based on the histogram, which of the following statements must be true? a the minimum price is $250,000. b the maximum price is $2,500,000. c the median price is not greater than $750,000. d the mean price is between $500,000 and $750,000.

Answer

Explanation:

Step1: Understand the histogram

The histogram shows price - ranges (in thousands of dollars) on the x - axis and the number of homes sold in each price - range on the y - axis. The first bar starts at 250 (thousands of dollars) but this does not mean the minimum price is exactly 250000. There could be homes sold at a lower price not captured in this histogram. Similarly, the last bar ends at 2500 (thousands of dollars), but there could be higher - priced homes not shown.

Step2: Calculate the position of the median

There are (n = 304) data points. The median position for a set of (n) data points (where (n) is even) is (\frac{n}{2}=152) and (\frac{n}{2}+ 1 = 153). We sum up the frequencies of the bars from the left. The first bar has 38 homes, the first two bars have (38 + 120=158) homes. So the median lies within the second price - range ((500 - 750) thousands of dollars). So the median price is not greater than 750000.

Step3: Analyze the mean

The mean is affected by the higher - priced homes in the right - hand side of the histogram. The large values in the higher price - ranges will pull the mean to the right. Since there are some very high - priced homes (as indicated by the small non - zero frequencies in the higher price - ranges), the mean is likely to be greater than 750000.

Answer:

C. The median price is not greater than $750,000.