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  • The mean and standard deviation of the ages of 200 individuals were found to be 50 years and 5 years, respectively. Later, it was discovered that an age of 50 years was wrongly recorded as 45 years

The mean and standard deviation of the ages of 200 individuals were found to be 50 years and 5 years, respectively. Later, it was discovered that an age of 50 years was wrongly recorded as 45 years. What are the correct mean and standard deviation, respectively?

 

Option: 1

50 years and 5 years


Option: 2

51 years and 5 years


Option: 3

50 years and 4 years


Option: 4

51 years and 4 years


Answers (1)

best_answer

To find the correct mean and standard deviation, we need to adjust the wrongly recorded age and recalculate these statistics.

First, let's adjust the age of 45 years to the correct age of 50 years.

The sum of the original 200 ages is 50 years \times 200 = 10,000 years.

We need to subtract the wrongly recorded age (45 years) and add the correct age (50 years) to the sum.

Corrected sum = (10,000 years - 45 years) + 50 years = 10,000 years - 45 years + 50 years = 10,005 years.

The correct mean is the corrected sum divided by the number of individuals (200).

Corrected mean = 10,005 years / 200 = 50.025 years.

Next, let's adjust the standard deviation. Since we only changed one age, the impact on the standard deviation is minimal.

The corrected standard deviation remains the same as the original standard deviation, which is 5 years.

Therefore, the correct mean is approximately 50.025 years, and the correct standard deviation is 5 years.

Among the given options, 50 years and 5 years is the closest to the correct mean and standard deviation.

 

Posted by

Rishabh

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