Table of Contents

- 1 What percentage of data values fall below the mean?
- 2 What is the percentage of observation?
- 3 What percentage of the area falls above the mean?
- 4 What percentage of values fall within this range?
- 5 How many observations fall below the median?
- 6 How do you calculate percentage below?
- 7 What percentage of the area falls within 1 standard deviation above and below the mean?
- 8 What is the percentage of values in the distribution between 17 and 32?
- 9 How can you find percentages of data away from the mean?
- 10 What is the range of z scores within 2 standard deviations?

## What percentage of data values fall below the mean?

In normally distributed data, about 34% of the values lie between the mean and one standard deviation below the mean, and 34% between the mean and one standard deviation above the mean.

## What is the percentage of observation?

The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

**How do you find the percent below z score?**

Subtract the value you just derived from 100 to calculate the percentage of values in your data set which are below the value you converted to a Z-score. In the example, you would calculate 100 minus 0.22 and conclude that 99.78 percent of students scored below 2,000.

### What percentage of the area falls above the mean?

The percentage of scores will fall above the mean value in a normal curve is 50%.

### What percentage of values fall within this range?

For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%.

**What percent of the data lie 1 standard deviation above the mean?**

Empirical Rule or 68-95-99.7% Rule Approximately 68% of the data fall within one standard deviation of the mean.

#### How many observations fall below the median?

It is observed that 3 observations of dataset fall below the mean. Therefore, it is not necessary that half of the observations fall below its mean value.

#### How do you calculate percentage below?

How to Calculate Percentage Decrease

- Subtract starting value minus final value.
- Divide that amount by the absolute value of the starting value.
- Multiply by 100 to get percent decrease.
- If the percentage is negative, it means there was an increase and not an decrease.

**How do you find area above and below z-score?**

To find the percentage of the area that lies “above” the z-score, take the total area under a normal curve (which is 1) and subtract the cumulative area to the left of the z-score.

## What percentage of the area falls within 1 standard deviation above and below the mean?

68%

The Empirical Rule or 68-95-99.7% Rule can give us a good starting point. This rule tells us that around 68% of the data will fall within one standard deviation of the mean; around 95% will fall within two standard deviations of the mean; and 99.7% will fall within three standard deviations of the mean.

## What is the percentage of values in the distribution between 17 and 32?

To solve this problem, note that 17-2=15, which is 3 standard deviations. The 68-95-99.7 rule states that 99.7% of the population will lie within 3 standard deviations of the mean; this means in this case that 99.7% lie between 2 and 17+15 = 32.

**How many values fall within one standard deviation of the mean?**

Approximately 68% of the data values will fall within 1 standard deviation of the mean, from 101 101 to 173 173. Approximately 95% of the data values will fall within 2 standard deviations of the mean, from 65 65 to 209 209.

### How can you find percentages of data away from the mean?

With the Empirical Rule, we can estimate the percentages of data values up to 3 standard deviations away from the mean. The Empirical Rule Calculator above will be able to tell you the percentage of values within 1, 2 or 3 standard deviations of the mean.

### What is the range of z scores within 2 standard deviations?

Within 2 standard deviations – This refers to the range of values between a z-score of -2 to a z-score of +2. And finally, within 3 standard deviations – This refers to the range of values between a z-score of -3 to a z-score of +3.