# 9.3.1. Collecting Data

The table below illustrates the amounts of three different kinds of stones stored in a warehouse, where the total number of stones is 15 000.

 Kinds of Stones Number of Stones First Kind Second Kind Third Kind 2 000 6 000 7 000

Given that a sample, which includes stones from all 3 kinds, is to be taken from the warehouse, and the number of stones taken from the third kind is 420, determine the total number of stones in the sample.

• A900
• B120
• C
6 300 000
• D420

### Example

The table below illustrates the amounts of three different kinds of stones stored in a warehouse, where the total number of stones is 15 000.

 Kinds of Stones Number of Stones First Kind Second Kind Third Kind 2 000 6 000 7 000

Given that a sample, which includes stones from all 3 kinds, is to be taken from the warehouse, and the number of stones taken from the third kind is 420, determine the total number of stones in the sample.

### Solution

When a society to be examined is made up of qualitative sets that have different characteristics, the society should be divided into homogeneous layers according to the characteristics. A researcher should then select a random sample from each layer that is proportional in size to the layer's size in the society. Suppose the total number of stones in the sample from the warehouse is . Solve for as follows.

Thus, the total number of stones that should be in the sample is 900.

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