Calculate the mean for the following data:
`{:(,"Wages per week upto Rs.",15,30,45,60,75,90,105,120),(,"No. of workers",12,30,65,107,157,202,222,230):}`

Answer

To calculate the mean for the given data, we will follow these steps:

### Step 1: Organize the Data
We have two sets of data: Wages per week (XI) and Number of Workers (FI).

- Wages per week (XI): 15, 30, 45, 60, 75, 90, 105, 120
- Number of Workers (FI): 12, 30, 65, 107, 157, 202, 222, 230

### Step 2: Calculate the Product of XI and FI
Next, we calculate the product of each wage and the corresponding number of workers (XI * FI):

- For 15: 15 * 12 = 180
- For 30: 30 * 30 = 900
- For 45: 45 * 65 = 2925
- For 60: 60 * 107 = 6420
- For 75: 75 * 157 = 11775
- For 90: 90 * 202 = 18180
- For 105: 105 * 222 = 23310
- For 120: 120 * 230 = 27600

Now, let's summarize this in a table format:

| Wages per week (XI) | No. of Workers (FI) | XI * FI |
|----------------------|---------------------|---------|
| 15 | 12 | 180 |
| 30 | 30 | 900 |
| 45 | 65 | 2925 |
| 60 | 107 | 6420 |
| 75 | 157 | 11775 |
| 90 | 202 | 18180 |
| 105 | 222 | 23310 |
| 120 | 230 | 27600 |

### Step 3: Calculate the Summation of FI and XI * FI
Now, we need to calculate the summation of FI and the summation of XI * FI.

- Summation of FI (Total number of workers):
\( 12 + 30 + 65 + 107 + 157 + 202 + 222 + 230 = 1025 \)

- Summation of XI * FI:
\( 180 + 900 + 2925 + 6420 + 11775 + 18180 + 23310 + 27600 = 91290 \)

### Step 4: Calculate the Mean
Now, we can calculate the mean using the formula:

\[ \text{Mean} = \frac{\Sigma (XI \cdot FI)}{\Sigma FI} \]

Substituting the values we calculated:

\[ \text{Mean} = \frac{91290}{1025} \approx 89.06 \]

### Final Result
The mean wages per week is approximately **89.06**.

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