232k views
5 votes
If nothing is known about the shape of the distribution of a quantitative variable, what percentage of data fall within 2 standard deviation of the mean?

User Chollida
by
8.3k points

2 Answers

6 votes

Answer:

95%

Step-by-step explanation:

I just took a test

User Uladzislau Vavilau
by
9.5k points
7 votes
At least 75% of the data will fall within 2 standard deviations of the mean. This is tricky problem. Usually when you're dealing with standard deviation, you have a bell curve, or something close to a bell curve and for such a data distribution, there will be approximately 95% of the data within 2 standard deviations of the mean. But if you don't know that you have a bell curve, you have to fall back to Chebyshev’s Theorem, which states that at least 75% of the data points will fall within 2 standard deviations of the mean for any set of numbers.
User Alif
by
8.7k points