SAT One-variable data Question

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Question 1 · Hard · MathMarch 2025 Batch 6 · Q14One-variable data: distributions and measures of center and spread · 0 solved

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Weight (pounds) The histogram summarizes a data set of the weights, in pounds, of 14 salmon. If an additional weight of 32 pounds is added to the original data set to create a new data set of 15 weights, which of the following measures must be less for the new data set than for the original data set? I. The median II. The mean

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Strategy

For a median question, track how the middle position changes when one value is added, especially whether the new value is an extreme. For a mean question, compare the new value to the original average: adding a value below the current mean lowers the mean, while adding a value above it raises the mean.

Hints (open one at a time)

Hint 1

First find the original data set size from the histogram, then think about where the middle values are.

Hint 2

Adding one data point changes the median position, but it affects the mean by pulling the average toward the new value.

Hint 3

Use the histogram to see whether 32 is below or above the existing weights, and use that to decide what happens to the mean.

Step-by-step Explanation

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