When analyzing the sample data from an experiment or research study, perhaps one of the most important statistical parameters is the mean: the numerical average of all the data points. However, statistical analysis is ultimately a theoretical model imposed on a set of concrete, physical data. To account for the inherent imprecision of statistical modeling, use confidence intervals to evaluate the reliability of the mean (and other parameters). A confidence interval is a range of values within which a parameter is likely to be found. The larger the interval, the higher the probability of it including the actual parameter.

## Calculate The Standard Deviation

### Step 1

Add together the value of every data point in the sample.

### Step 2

Divide this sum by the total number of data points. This is the mean value for the sample.

### Step 3

Subtract the mean from the lowest value of all the data points. For example, in the set of five data points with values of 3, 6, 11, 2 and 4, the mean would be 5.2, or (3+6+11+2+4)/5 = (26)/5 = 5.2. Since "2" is the lowest value, subtract 5.2 from 2 to get -3.2.

### Step 4

Square this value and write down the result.

### Step 5

Repeat Steps 3 and 4 for every data point in the entire sample.

### Step 6

Add together all of the values you wrote down in Step 4.

### Step 7

Divide the total from Step 6 by the total number of data points.

### Step 8

Find the square root of the result from Step 7. The result will be the standard deviation for the sample.

### Step 9

Divide the standard deviation by the square root of the total number of data points. The result is called the standard error of the mean.

## Calculating the Confidence Interval

### Step 1

Dtermine the critical value or "z" for the specific percentage you want the interval to be. Do this by accessing an online table (see Resources).

### Step 2

Scroll down the second calculator on the page and check the box next to "Between."

### Step 3

In the text field next to "Area", enter the percentage you want (in decimal form). For example, if you want a 95 percent confidence interval, type 0.95. If you want a 99 percent confidence interval, type 0.99.

### Step 4

Write down the number that appears next to "Between." This is the critical value for the interval.

### Step 5

Multiply the critical value by the standard error of the mean (calculated in Section 1, Step 9).

### Step 6

Subtract the result from the parameter you want to set the confidence interval around (the mean). This is the "lower boundary" of the confidence interval.

### Step 7

Add the result from Section 2, Step 5 to the parameter. This is the upper boundary of the confidence interval.