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12 Aug 2026, 01:57
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The table below shows the number of eggs collected monthly from five farms during a 6-month period.
The standard deviation of the numbers of eggs collected monthly during the period was greatest for which of the five farms?
A. Green Pastures
B. Sunny Meadows
C. Willow Creek
D. Maple Lane
E. Golden Harvest
| Farm | Monthly eggs | |
|---|---|---|
| Green Pastures | 250, 300, 300, 275, 250, 275 | |
| Sunny Meadows | 400, 500, 450, 400, 450, 500 | |
| Willow Creek | 300, 325, 350, 325, 350, 300 | |
| Maple Lane | 200, 100, 400, 200, 400, 500 | |
| Golden Harvest | 200, 250, 300, 350, 400, 300 |
The standard deviation of the numbers of eggs collected monthly during the period was greatest for which of the five farms?
A. Green Pastures
B. Sunny Meadows
C. Willow Creek
D. Maple Lane
E. Golden Harvest
13 Aug 2026, 01:32
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This question might seem difficult, but in reality, it is very easy if you know an important concept related to Standard Deviation.
You DO NOT need to calculate using the formula for Standard Deviation:
Standard Deviation essentially measures how spread out numbers are from their mean.
Compare the ranges:
Green Pastures: 250 - 300 -> range 50
Sunny Meadows: 400 - 500 -> range 100
Willow Creek: 300 - 350 -> range 50
Maple Lane: 100 - 500 -> range 400
Golden Harvest: 200 - 400 -> range 200
Clearly, Maple Lane has by far the greatest spread.
Hence, the correct answer is Option D - Maple Lane.
Hope this helps!
You DO NOT need to calculate using the formula for Standard Deviation:
Standard Deviation essentially measures how spread out numbers are from their mean.
Compare the ranges:
Green Pastures: 250 - 300 -> range 50
Sunny Meadows: 400 - 500 -> range 100
Willow Creek: 300 - 350 -> range 50
Maple Lane: 100 - 500 -> range 400
Golden Harvest: 200 - 400 -> range 200
Clearly, Maple Lane has by far the greatest spread.
Hence, the correct answer is Option D - Maple Lane.
Hope this helps!
13 Aug 2026, 14:12
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The range shortcut above gets you there fast, and on the real test that is exactly the move, but I want to show the actual numbers so you can see why it works here.
1. Standard deviation measures spread from the mean, and Maple Lane's range of 400 versus everyone else topping out around 100 to 200 is a big enough gap that range alone gets you to D safely.
2. Just to confirm with real numbers: Maple Lane's mean is 300, deviations are -200, -100, 100, -100, 100, 200, square and average those and you get a variance near 20,000, so a standard deviation around 141.
3. Compare that to Golden Harvest, which has the second largest range at 200. Its mean is also 300, but its numbers climb steadily instead of swinging wide, deviations of -100, -50, 0, 50, 100, 0, giving a variance near 4,167 and a standard deviation near 65. Not close.
Answer is D.
The one time range alone can mislead you is when two farms have similar ranges but very different distributions inside that range, tight in the middle versus spread evenly. Worth doing the quick gut check on the actual numbers when ranges are close, and trusting the shortcut when one range is this obviously bigger.
1. Standard deviation measures spread from the mean, and Maple Lane's range of 400 versus everyone else topping out around 100 to 200 is a big enough gap that range alone gets you to D safely.
2. Just to confirm with real numbers: Maple Lane's mean is 300, deviations are -200, -100, 100, -100, 100, 200, square and average those and you get a variance near 20,000, so a standard deviation around 141.
3. Compare that to Golden Harvest, which has the second largest range at 200. Its mean is also 300, but its numbers climb steadily instead of swinging wide, deviations of -100, -50, 0, 50, 100, 0, giving a variance near 4,167 and a standard deviation near 65. Not close.
Answer is D.
The one time range alone can mislead you is when two farms have similar ranges but very different distributions inside that range, tight in the middle versus spread evenly. Worth doing the quick gut check on the actual numbers when ranges are close, and trusting the shortcut when one range is this obviously bigger.
