The scores on the final exam in a course have approximately a bell-shaped distribution. The mean score was 72, the highest score was 99, and the lowest score was 41.
Use the value of the range (58) to estimate the value of the standard deviation. (Round your answer to the nearest tenth.)
Take the range and divide by 4 for an estimate of the standard deviation.
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To estimate the value of the standard deviation using the range, we can use the following formula:
Range = 4 * Standard Deviation
Given that the range is 58, we can plug it into the formula and solve for the standard deviation:
58 = 4 * Standard Deviation
Dividing both sides of the equation by 4:
Standard Deviation = 58 / 4
Standard Deviation ≈ 14.5
Therefore, the estimated value of the standard deviation is approximately 14.5.
To estimate the value of the standard deviation using the range, we can use a rough approximation called the Empirical Rule. The Empirical Rule states that in a bell-shaped distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the range is equal to 2 times the standard deviation, we can divide the range by 2 to estimate the standard deviation.
In this case, the range is 58. So we can estimate the standard deviation as 58/2 = 29.
Therefore, the estimated value of the standard deviation is 29.