Often you may want to calculate the standard deviation of a frequency distribution in Excel.

For example, suppose you have the following frequency distribution:

The following step-by-step example shows how to calculate the standard deviation of this frequency distribution in Excel.

**Step 1: Enter Values for Frequency Distribution**

First, we’ll enter the class limits and frequency values for our frequency distribution:

**Step 2: Calculate Mean of Frequency Distribution**

We can use the following formula to estimate the mean of our frequency distribution:

**Mean:** Σm_{i}n_{i} / N

where:

**m**The midpoint of the i_{i}:^{th}group**n**The frequency of the i_{i}:^{th}group**N:**The total sample size

To apply this formula in Excel, we will type the following formulas into cells **D2**, **E2**, and **F2**:

**D2**: =AVERAGE(A2:B2)**E2**: =D2*C2**F2**: =SUM($E$2:$E$6)/SUM($C$2:$C$6)

We will then click and drag these formulas down to each remaining cell in each column:

**Step 3: Calculate Standard Deviation of Frequency Distribution**

**Standard Deviation:** √Σn_{i}(m_{i}-μ)^{2} / (N-1)

where:

**n**The frequency of the i_{i}:^{th}group**m**The midpoint of the i_{i}:^{th}group**μ**: The mean**N:**The total sample size

To apply this formula in Excel, we will type the following formulas into cells **G2**, **H2**, and **I2**:

**G2**: =D2-F2**H2**: =G2^2**I2**: =C2*H2

We will then click and drag these formulas down to each remaining cell in each column:

Lastly, we can type the following formula into cell **B8** to calculate the standard deviation of this frequency distribution:

=SQRT(SUM(I2:I6)/(SUM(C2:C6)-1))

The following screenshot shows how to use this formula in practice:

The standard deviation of this frequency distribution turns out to be **9.6377**.

**Additional Resources**

The following tutorials explain how to perform other common tasks in Excel: