(i) Find the mean of children per family from data given below :
`{:("No. of children " ,0,1,2,3,4,5),("No. of families ",5,11,25,12,5,2):}`
(ii) which mathematical concept is used in this problem ?
(iii) Which value is discussed here ?

Answer

To solve the problem step by step, we will find the mean number of children per family using the given data.

### Step 1: Understand the Data
We have two sets of data:
- Number of children (xi): 0, 1, 2, 3, 4, 5
- Number of families (fi): 5, 11, 25, 12, 5, 2

### Step 2: Create a Table
We will create a table to calculate the product of the number of children and the number of families.

| No. of Children (xi) | No. of Families (fi) | xi * fi |
|-----------------------|----------------------|---------|
| 0 | 5 | 0 * 5 = 0 |
| 1 | 11 | 1 * 11 = 11 |
| 2 | 25 | 2 * 25 = 50 |
| 3 | 12 | 3 * 12 = 36 |
| 4 | 5 | 4 * 5 = 20 |
| 5 | 2 | 5 * 2 = 10 |

### Step 3: Calculate the Products
Now, we will calculate the products (xi * fi) for each row:
- For 0 children: 0 * 5 = 0
- For 1 child: 1 * 11 = 11
- For 2 children: 2 * 25 = 50
- For 3 children: 3 * 12 = 36
- For 4 children: 4 * 5 = 20
- For 5 children: 5 * 2 = 10

### Step 4: Sum the Values
Next, we will sum the values of fi and xi * fi:
- Summation of fi = 5 + 11 + 25 + 12 + 5 + 2 = 60
- Summation of xi * fi = 0 + 11 + 50 + 36 + 20 + 10 = 127

### Step 5: Calculate the Mean
Now, we can calculate the mean using the formula:
\[ \text{Mean} = \frac{\Sigma (xi \cdot fi)}{\Sigma fi} = \frac{127}{60} \]

Calculating this gives:
\[ \text{Mean} \approx 2.12 \]

### Step 6: Conclusion
The mean number of children per family is approximately 2.12.

### Answer to Part (ii)
The mathematical concept used in this problem is the **mean of ungrouped data**.

### Answer to Part (iii)
The value discussed here is related to **population control**, indicating that for progress, the population should not increase but rather decrease.

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