218k views
1 vote
In a normal distribution, 95% of the data falls within 2 standard deviations of the mean.

Option 1: True
Option 2: False

1 Answer

6 votes

Final answer:

The statement that 95% of the data in a normal distribution falls within two standard deviations of the mean is true and is an aspect of the Empirical Rule applicable only to bell-shaped, symmetrical distributions.

Step-by-step explanation:

The statement in question is true. In a normal distribution, also known as a Gaussian distribution, approximately 95% of the data falls within two standard deviations of the mean. This is part of what is referred to as the Empirical Rule or the 68-95-99.7 rule, which describes the proportion of values that lie within each standard deviation for a normal distribution. Specifically, it states that about 68% falls within the first standard deviation, 95% within two standard deviations, and more than 99% within three standard deviations of the mean.It's crucial to recognize that these percentages hold true only for distributions that are bell-shaped and symmetric. If a dataset doesn't follow a normal distribution, the percentages will differ. This empirical observation is a foundational concept in statistics and is particularly useful when making inferences about a population based on sample data.

User Rui Marinho
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories