Key Takeaways. The
What is standard deviation? Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.
The Empirical Rule is a statement about normal distributions. Your textbook uses an abbreviated form of this, known as the 95% Rule, because 95% is the most commonly used interval. The 95% Rule states that approximately 95% of observations fall within two standard deviations of the mean on a normal distribution.
Answer and Explanation:
In a normal distribution, about 95% of the data are within two standard deviations of the mean. This is according to 68-95-99.7 empirical rule of standard score. The rule states that; About 68% of the data is contained within one standard standard of the mean.
The empirical rule (also called the "68-95-99.7 rule") is a guideline for how data is distributed in a normal distribution. The rule states that (approximately): - 68% of the data points will fall within one standard deviation of the mean. - 95% of the data points will fall within two standard deviations of the mean.
The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution: Around 68% of values are within 1 standard deviation of the mean. Around 95% of values are within 2 standard deviations of the mean. Around 99.7% of values are within 3 standard deviations of the mean.
Empirical Rule or 68-95-99.7% Rule
Approximately 68% of the data fall within one standard deviation of the mean. Approximately 95% of the data fall within two standard deviations of the mean. Approximately 99.7% of the data fall within three standard deviations of the mean.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
Rules of thumb regarding spread
At least 75% of the data will be within two standard deviations of the mean. At least 89% of the data will be within three standard deviations of the mean. Data beyond two standard deviations away from the mean is considered "unusual" data.
95% of the data in a data set will fall within two standard deviations of the mean (between -2sd and 2sd) 99.7% of the data in a data set will fall within three standard deviations of the mean (between -3sd and 3sd)
95.4% of data values are within 2 standard deviations of the mean (-2 to +2) 99.7% of data values are within 3 standard deviations of the mean (-3 to +3)
For instance, 1.96 (or approximately 2) standard deviations above and 1.96 standard deviations below the mean (±1.96SD mark the points within which 95% of the observations lie.
For the standard normal distribution, 68% of the observations lie within 1 standard deviation of the mean; 95% lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean.
The 68-95-99 rule
It says: 68% of the population is within 1 standard deviation of the mean. 95% of the population is within 2 standard deviation of the mean. 99.7% of the population is within 3 standard deviation of the mean.
For example, a score that is 2 standard deviations below the mean would have a percentile rank of 2 (0.13 + 2.14 = 2.27). In other words, just over 2% of the area underneath the normal curve is to the left of a standard score that is 2 standard deviations below the mean.
One question students often have is: What is considered a good value for the standard deviation? What is this? The answer: A standard deviation can't be “good” or “bad” because it simply tells us how spread out the values are in a sample.
A score that is two Standard Deviations above the Mean is at or close to the 98th percentile (PR = 98). A score that is two Standard Deviations below the Mean is at or close to the 2nd percentile (PR =2).
About 95% of the values lie within two standard deviations of the mean, that is, between (ˉx−2σ) and (ˉx+2σ) . (In the figure, this is the sum of the pink and blue regions: 34%+34%+13.5%+13.5%=95% .) About 99.7% of the values lie within three standard deviations of the mean, that is, between (ˉx−3σ) and (ˉx+3σ) .
At least 75% of the data is within 2 standard deviations of the mean. At least 89% of the data is within 3 standard deviations of the mean. At least 95% of the data is within 4 1/2 standard deviations of the mean.
Values that are greater than +3 standard deviations from the mean, or less than -3 standard deviations, are included as outliers in the output results.
It's basically the same as the first instance, only this time we're looking at two standard deviations above and below the mean. For any normal distribution, approximately 95 percent of the observations will fall within this area.
If we wanted to specify the middle 95% of a normal distribution, then the magical number is 1.96: 95% of the probability mass in a normal distribution falls within 1.96 standard deviations on either side of it. For example, consider again the /t/ VOT distribution, with a mean of 0.070 and standard deviation of 0.015.
In a normal curve, the percentage of scores which fall between -1 and +1 standard deviations (SD) is 68%.