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We want to determine the mean and standard deviation of ungrouped data in practically all circumstances. However, how can you do that with grouped data?

## Grouped Data Mean and Standard Deviation

Let’s look at an example of how to compute mean and SD.

How to Calculate Root Mean Square Error (RMSE) in R »

### Grouped Data Mean

The formula for grouped mean is

`Mean: Σmini / N`

where:

mi: Midpoint of the ith group

ni: Frequency of the ith group

N: Total sample size

The midpoint is determined by averaging the range’s bottom and upper values.

`Mean=(42+244+303+141+814.5)/29=53.26`

Grouped data set mean is 53.26.

### Grouped Data Standard Deviation

Let’s look at the formula for computing the standard deviation of grouped data.

How to Calculate Mean Absolute Percentage Error (MAPE) in R »

`Standard Deviation: Sqrt(Σni(mi-μ)2 / (N-1))`

where:

ni: Frequency of the ith group

mi: Midpoint of the ith group

μ: Average value

N: Total sample size

Let’s execute the formula.

`Standard Deviation=sqrt(169+4050+11881.5+9384.5+59780.25)/28=55.18`

Grouped data standard is 55.18.

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