# Algebra 1 : How to find standard deviation

## Example Questions

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### Example Question #11 : How To Find Standard Deviation

Find the standard deviation of the data set:

Explanation:

Write the formula of standard deviation.

Determine the mean, .

Subtract each number in the dataset from the mean and square each result.

This is the  term.

Find the mean of the squared differences, or the variance.

This is the  term.

Square root the variance for the standard deviation.

### Example Question #12 : How To Find Standard Deviation

Find the standard deviation. Round your answer to the nearest tenth.

Explanation:

To find standard deviation, we apply this formula: .

n represents how many data in the set.

represents the average of the data in the set.

is any data in the set.

is summation of the difference between average and any data value squared.

So the mean is . Now, we apply the formula.

### Example Question #13 : How To Find Standard Deviation

Find the standard deviation. Round your answer to the nearest tenth.

Explanation:

To find standard deviation, we apply this formula: .

n represents how many data in the set.

represents the average of the data in the set.

is any data in the set.

is summation of the difference between average and any data value squared.

So the mean is . Now, we apply the formula.

### Example Question #14 : How To Find Standard Deviation

Find the standard deviation of the following set of numbers:

Explanation:

To find standard deviation, we will follow these steps:

1. Find the mean of the original set of numbers.
2. Subtract the mean from each of the original numbers.
3. Square each number.
4. Find the mean of the new set of numbers.
5. Take the square root of the mean.

So, we will take this step by step.

## STEP 2

7, 10, 13

(7-10), (10-10), (13-10)

-3, 0, 3

9, 0, 9

## STEP 5

Thefore, the standard deviation is .

### Example Question #1991 : Algebra 1

Find the standard deviation of the following set of numbers:

Explanation:

To solve, you must use the following equation:

where,

Thus,

### Example Question #11 : How To Find Standard Deviation

Find the standard deviation of the following set of numbers.

Explanation:

To solve, simply use the formula for standard deviation. Thus,

where xm is the mean. Thus,

### Example Question #17 : How To Find Standard Deviation

Find the standard deviation of the following data set:

4, 2, 6, 8, 8, 2, 8, 10, 6.

Explanation:

To find the standard deviation, we will go through a few steps.

## Step 1:  Find the mean.

We will find the mean of the data set.

## Step 2:  Subtract the mean from each number in the data set.

We will now take each number in the data set and subtract the mean from it.

Giving us a new data set of -2, -4, 0, 2, 2, -4, 2, 4, 0.

## Step 3:  Square each number in the data set.

Giving us a new data set of 4, 16, 0, 4, 4, 16, 4, 16, 0.

## Step 4:  Add each number in the data set together.

Giving us an answer of 64.

## Step 5:  Take the square root of the answer.

That is the standard deviation!  So, the standard deviation of the data set

4, 2, 6, 8, 8, 2, 8, 10, 6

is 8.

### Example Question #18 : How To Find Standard Deviation

If the variance of a set of sample data is , what is the standard deviation?

Explanation:

The formula for finding the standard deviation given the variance is:

Substitute the variance.

The standard deviation is .

### Example Question #19 : How To Find Standard Deviation

Approximate the standard deviation of the given set of numbers to three decimal places:

Explanation:

Write the formula for standard deviation.

represents the total numbers in the data set:

is the mean:

Find the mean of the squared differences.   Subtract each number in the data set with the mean, square the quantities, and take the average.

This will be the variance:

The standard deviation is the square root of the variance, which is the square root of this fraction.

### Example Question #20 : How To Find Standard Deviation

If the variance of a data set is 60, what must be the standard deviation?  Round to three decimal places.