Question

Find the geometric mean for the following data:

Marks 4 - 8 8 - 12 12 - 16 16 - 20 20 - 24 24 - 28 28 – 32 32 - 36 36 – 40

Frequency 6 10 18 30 15 12 10 6 2​

Answer 1

Answer:

60

Step-by-step explanation:

30×2=60 it's easy if incorrect use calculater

Answer 2

The geometric mean for the given set of data is 324.26494.

Given:

The table containing the marks and corresponding frequency of students is given.

To Find:

We have to find the geometric mean for the given data.

Solution:

The geometric mean, or GM, is usually calculated by multiplying all the numbers in the given data set and then taking the nth root of the obtained result.

Here, the marks are represented in ranges. So the following method is employed to find the GM:

The mid value of given frequency (f), log of x and f.log x are calculated as in the table below.

The equation for GM = $Antilog\frac{Σ (f.log x)}{n}$, where $n = f1 + f2 +.....+ fn.$

Consider the below table.

Σ (f.log x) = 273.696

n = 109

∴, GM = $Antilog\frac{273.696}{109} = Antilog(2.5109) = 324.26494.$

Hence, the geometric mean for the provided set of data is 324.26494.

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