The mean and standard deviation of the heights of 200 students were found to be 170 cm and 5 cm, respectively. Later, it was discovered that a measurement of 170 cm was wrongly recorded as 180 cm. What are the correct mean and standard deviation, respectively?
170 cm and 5 cm
169 cm and 5 cm
170 cm and 4 cm
169 cm and 4 cm
To find the correct mean and standard deviation, we need to adjust the wrongly recorded measurement and recalculate these statistics.
First, let's adjust the measurement of 180 cm to the correct measurement of 170 cm.
The sum of the original 200 heights is 170 200 = 34,000 cm.
We need to subtract the wrongly recorded height (180 cm) and add the correct height (170 cm) to the sum.
Corrected sum = (34,000 - 180) + 170 = 34,000 - 180 + 170 = 34,000.
The correct mean is the corrected sum divided by the number of students (200).
Corrected mean = 34,000 / 200 = 170 cm.
Next, let's adjust the standard deviation. Since we only changed one measurement, the impact on the standard deviation is minimal.
The corrected standard deviation remains the same as the original standard deviation, which is 5 cm.
Therefore, the correct mean is 170 cm, and the correct standard deviation is 5 cm.
Among the given options, 170 cm and 5 cm is the correct choice.
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