Mean ±2 σ under normal curve covers:

Question

Question

This question was previously asked in

SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)

Answer 1

The correct answer is 95.45% area

Key Points

In a normal distribution, the range of values that are defined by the mean ±2 standard deviations (±2σ) encompasses approximately 95.45% of the total area under the curve.
This statistical property is commonly referred to as the "empirical rule" or the "68-95-99.7 rule." It provides a rough estimation of the proportion of data points that fall within a certain number of standard deviations from the mean in a normal distribution.
According to this rule:
- Approximately 68% of the data falls within one standard deviation (±1σ) of the mean. This means that the majority of the data points (about 68%) are located within a range that extends one standard deviation on either side of the mean.
- Approximately 95% of the data falls within two standard deviations (±2σ) of the mean. In other words, the vast majority of the data points (about 95%) are contained within a range that extends two standard deviations on either side of the mean.
- Approximately 99.7% of the data falls within three standard deviations (±3σ) of the mean. This indicates that almost all of the data points (about 99.7%) are found within a range that extends three standard deviations on either side of the mean.

The empirical rule provides a convenient way to estimate the spread and distribution of data in a normal distribution.
It highlights the fact that data tends to cluster around the mean and becomes less frequent as it moves farther away from the mean, following a symmetric pattern.
While the empirical rule provides only rough estimates, it is often applied to many real-world datasets that exhibit a normal distribution or approximate normality.

Consequently, when considering the range of mean ±2σ, it encompasses an approximate area of 95.45% under the normal curve.