# Geometric Mean Calculator for Grouped Data with Examples

## Geometric mean for grouped data

Geometric mean is another measure of central tendency. Geometric mean is used when the data is in terms of rates and ratios.

Let $(x_i,f_i), i=1,2, \cdots , n$ be given frequency distribution. The geometric mean of $X$ is denoted by $GM$ and is given by

 $$\begin{eqnarray*} GM& =\bigg(\prod_{i=1}^n x_i^{f_i}\bigg)^{1/N}\\ \therefore \log (GM) &=\frac{1}{N}\sum_{i=1}^n f_i\log(x_i) \end{eqnarray*}$$

where,$N=\sum_i f_i$ total number of observations.

## Geometric Mean Calculator

Use geometric mean calculator to calculate the Geometric Mean for grouped data and frequency distribution.

Geometric Mean Calculator for Grouped Data
Type of Frequency Distribution DiscreteContinuous
Enter the Classes for X (Separated by comma,)
Enter the frequencies (f) (Separated by comma,)
Geometic Mean Results
Number of Observation (N):
Geometric Mean :
frequency distribution :

## How to find geometric mean of grouped data?

Step 1 - Select type of frequency distribution (Discrete or continuous)

Step 2 - Enter the Range or classes (X) seperated by comma (,)

Step 3 - Enter the Frequencies (f) seperated by comma

Step 4 - Click on "Calculate" for geometric mean calculation

Step 5 - Gives output as number of observation (n)

Step 6 - Calculate geometric mean

Step 7 - Display frequency distribution

## Geometric Mean for Grouped Data Example 1

Compute geometric mean for the following frequency distribution.

x 5-8 9-12 13-16 17-20 21-24
f 2 13 21 14 5

#### Solution

Class Boundries mid-value ($x_i$) Freq ($f_i$) $log(x_i)$ $f_i*log(x_i)$
4.5-8.5 6.5 2 1.8718 3.7436
8.5-12.5 10.5 13 2.3514 30.5682
12.5-16.5 14.5 21 2.6741 56.1561
16.5-20.5 18.5 14 2.9178 40.8492
20.5-24.5 22.5 5 3.1135 15.5675
tot Total 55 146.8846

The log of geometric mean is

 \begin{aligned} \log (GM) &=\frac{1}{N}\sum_{i=1}^n f_i\log(x_i)\\ &=\frac{146.8846}{55}\\ &=2.6706 \end{aligned}

The geometric mean is

 \begin{aligned} GM & =\exp(\log (GM))\\ &=\exp(2.6706)\\ &=14.4486 \end{aligned}

## Geometric Mean for Grouped Data Example 2

Find the geometric mean of distribution of weights of 75 students at virtual University in the table:

Weight Frequency
110-119 1
120-129 4
130-139 17
140-149 28
150-159 25

#### Solution

Class Boundries mid-value ($x_i$) Freq ($f_i$) $log(x_i)$ $f_i*log(x_i)$
109.5-119.5 114.5 1 4.7406 4.7406
119.5-129.5 124.5 4 4.8243 19.2972
129.5-139.5 134.5 17 4.9016 83.3272
139.5-149.5 144.5 28 4.9733 139.2524
149.5-159.5 154.5 25 5.0402 126.005
tot Total 75 372.6224

The log of geometric mean is

 \begin{aligned} \log (GM) &=\frac{1}{N}\sum_{i=1}^n f_i\log(x_i)\\ &=\frac{372.6224}{75}\\ &=4.9683 \end{aligned}

The geometric mean is

 \begin{aligned} GM & =\exp(\log (GM))\\ &=\exp(4.9683)\\ &=143.7822 \;\; minutes \end{aligned}

## Geometric Mean for Grouped Data Example 3

Following is the frequency distribution about the weight of earheads in grams:

60-80 22
80-100 38
100-120 45
120-140 35
140-160 20

Calculate geometric mean for the given frequency distribution.

#### Solution

Class Boundries mid-value ($x_i$) Freq ($f_i$) $log(x_i)$ $f_i*log(x_i)$
109.5-119.5 70 22 4.2485 93.467
119.5-129.5 90 38 4.4998 170.9924
129.5-139.5 110 45 4.7005 211.5225
139.5-149.5 130 35 4.8675 170.3625
149.5-159.5 150 20 5.0106 100.212
tot Total 160 746.5564

The log of geometric mean is

 \begin{aligned} \log (GM) &=\frac{1}{N}\sum_{i=1}^n f_i\log(x_i)\\ &=\frac{746.5564}{160}\\ &=4.666 \end{aligned}

The geometric mean is

 \begin{aligned} GM & =\exp(\log (GM))\\ &=\exp(4.666)\\ &=106.2718 \;\; grams \end{aligned}

## Geometric Mean for Grouped Data Example 4

For the following data about the diameter (in cm) of defective screw, calculate geometric mean.

Diameter (in cm) no. of defective screw
5 5
15 10
25 12
35 8
45 3

#### Solution

$x_i$ Freq ($f_i$) $log(x_i)$ $f_i*log(x_i)$
5 5 1.6094 8.047
15 10 2.7081 27.081
25 12 3.2189 38.6268
35 8 3.5553 28.4424
45 3 3.8067 11.4201
tot Total 38 113.6173

The log of geometric mean is

 \begin{aligned} \log (GM) &=\frac{1}{N}\sum_{i=1}^n f_i\log(x_i)\\ &=\frac{113.6173}{38}\\ &=2.9899 \end{aligned}

The geometric mean is

 \begin{aligned} GM & =\exp(\log (GM))\\ &=\exp(2.9899)\\ &=19.8837 \;\; cm \end{aligned}

## Conclusion

In this tutorial, you learned about formula for geometric mean for grouped data and how to calculate geometric mean for grouped data. You also learned about how to solve numerical problems based on geometric mean for grouped data.