The following chart shows the selling price ($000) of houses sold in the Billings, Montana area.Based on the data presented on the chart above, please answer the following question.Always provide your answer as a number, without any units. Note that the selling price is in thousand dollars.How many homes sold for not more than $280 000?

Question

BlackTom AI · Accepted Answer

First, identify what the question asks: the number of homes sold for not more than $280,000, noting that prices are in $1000s. On the chart, the selling price values (in $000) are 0, 50, 100, 150, 200, 250, 300, and 350 with corresponding cumulative frequencies (left axis) of 0, 20, 60, 90, 140, 160, 180, and 200 respectively. Since 280 is between 250 and 300, we interpolate between the points at 250 and 300.

Between 250 and 300 (in thousand dollars), the cumulative frequency increases from 160 to 180, a rise of 20 over a price change of 50 (i.e., slope = 20/50 = 0.4 per thousand dollars).

The target price is 280, which is 30 above 250. Applying the proportional increase: 30 * 0.4 = 12. Add this to the 160 at 250 to estimate the cumulative frequency at 280: 160 + 12 = 172.

Thus, the estimated number of homes sold for not more than $280,000 is approximately 172. This result comes from linear interpolation between the known data points at 250k and 300k, assuming a fairly steady rate of increase in the cumulative frequency within that interval.

Note: If the chart were read discretely only at the marked prices without interpolation, one might report 160 at 250k, but the more precise approach uses interpolation to estimate the value at 280k.

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