Calculate the price index number by simple average of relative method for the data of Ex. 2.

Answer

To calculate the price index number using the simple average of the relative method, we will follow these steps:

### Step 1: Write down the formula
The formula for the price index number (P01) using the simple average of the relative method is:
\[ P01 = \frac{\sum \left(\frac{P1}{P0}\right) \times 100}{n} \]
where \(P0\) is the price in the base year, \(P1\) is the price in the current year, and \(n\) is the number of commodities.

### Step 2: Create a table for the commodities
We will create a table to organize the data for each commodity, including \(P0\) and \(P1\).

| Commodity | \(P0\) | \(P1\) |
|-----------|--------|--------|
| A | 20 | 25 |
| B | 30 | 30 |
| C | 10 | 15 |
| D | 25 | 35 |
| E | 40 | 45 |
| F | 50 | 55 |

### Step 3: Calculate the relative prices
Next, we will calculate the relative price for each commodity using the formula \(\frac{P1}{P0} \times 100\).

| Commodity | \(P0\) | \(P1\) | \(\frac{P1}{P0} \times 100\) |
|-----------|--------|--------|-------------------------------|
| A | 20 | 25 | \(\frac{25}{20} \times 100 = 125\) |
| B | 30 | 30 | \(\frac{30}{30} \times 100 = 100\) |
| C | 10 | 15 | \(\frac{15}{10} \times 100 = 150\) |
| D | 25 | 35 | \(\frac{35}{25} \times 100 = 140\) |
| E | 40 | 45 | \(\frac{45}{40} \times 100 = 112.5\) |
| F | 50 | 55 | \(\frac{55}{50} \times 100 = 110\) |

### Step 4: Sum the relative prices
Now, we will sum the relative prices calculated in the previous step:
\[ \text{Sum} = 125 + 100 + 150 + 140 + 112.5 + 110 = 737.5 \]

### Step 5: Calculate the number of commodities
Count the number of commodities, \(n\):
\[ n = 6 \]

### Step 6: Calculate the price index number
Now, we can substitute the values into the formula:
\[ P01 = \frac{737.5}{6} = 122.92 \]

### Final Answer
The price index number is **122.92**.

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