Analyze the summary statistics table above to compare the price distribution of new and old houses. Prices are recorded in thousands of dollars. Which of the following statement(s) are FALSE? (Multiple selections allowed)

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BlackTom AI · Accepted Answer

Question restatement: You are asked to analyze a summary statistics table (not shown here) that compares the price distribution of new and old houses, with prices in thousands of dollars. The question asks which of the statements are FALSE, and multiple selections are allowed. Answer options:

- a. Both distributions are symmetric.
- b. The price distribution of new houses is less variable than the price distribution of old houses.
- c. Old houses tend to be less expensive according to the measures of central location.
- d. 50% of old houses cost less than $1.175 million.

How to evaluate each option if you had the table:

Option a: "Both distributions are symmetric." To judge symmetry, you would compare skewness or the shape of each distribution (e.g., histogram, symmetry around the mean or median, similar tails on both sides). If either distribution shows a notable skew (long tail to one side, or unequal left/right halves), this statement would be false for that distribution. If both distributions appear roughly symmetric, the statement could be true. Since you must declare if the statement is false, you would verify symmetry for both and see if the conjunction holds. Note that even if one distribution is symmetric and the other is not, the statement as a whole would be false.

Option b: "The price distribution of new houses is less variable than the price distribution of old houses." Variability can be assessed via standard deviation, interquartile range, or range. To determine this, you would compare the spread metrics for new versus old houses. If the spread metric for new houses is smaller than that for old houses, the statement would be true; if not, it would be false. Consider whether outliers might affect the range or whether robust measures (IQR) tell a different story than the full range.

Option c: "Old houses tend to be less expensive according to the measures of central location." Central location typically refers to the mean or median. You would compare the central tendency of old vs. new houses. If old houses have a lower mean or median price than new houses, this statement would be true; if old houses have a higher or similar central tendency, it would be false. Remember that “tend to be less expensive” depends on which central measure you reference and how the distributions compare.

Option d: "50% of old houses cost less than $1.175 million." Interpreting this requires the 50th percentile (the median) of the old-house price distribution. If the old-house median price is below 1,175 thousand (i.e., $1.175 million), this statement would be true; if the median is at or above 1,175 thousand, it would be false. Note that rounding and units are important: prices are in thousands, so 1.175 million corresponds to 1,175 on the same scale.

Important considerations when data is missing:
- Since the actual summary statistics table is not provided in this prompt, you cannot definitively classify any option as true or false without inspecting the table's values (skewness indicators, variability measures, central-tendency measures, and the old-house percentile).
- If you later obtain the table, apply the criteria above to each option, and mark the ones that do not hold as the false statements.

Worked heuristics to apply once data is available:
- For symmetry: look at skewness values near zero and comparable left/right tails in a histogram or density plot; if skewness is noticeably positive or negative, symmetry is violated.
- For variability: directly compare standard deviations or IQRs; a smaller value indicates less variability, but also consider whether outliers distort the range.
- For central location: compare medians or means; a clear ordering (old vs new) determines whether the statement about which group is cheaper holds.
- For percentile statements: identify the old-house median price and compare it to 1,175 (in thousands) to determine truth value.

In summary, to determine which statements are FALSE, you must consult the table and apply these checks. Without the table, provide only the evaluative framework and the exact criteria you would use to decide, as shown above.

MCD2080 - T1 - 2025 LECTURE 03 LESSON 2: FAT 1 T1 2025

Analyze the summary statistics table above to compare the price distribution of new and old houses. Prices are recorded in thousands of dollars. Which of the following statement(s) are FALSE? (Multiple selections allowed)

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