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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.

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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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The post Grouped Data Mean and Standard Deviation Calculator appeared first on finnstats.