Number of telephone cells received in 245 succesive one minute intervals at an exchange is given belwo in the following frequency distribution.
`{:("Number of calls",0,1,2,3,4,5,6,7),("Frequency",14,21,25,43,51,40,39,12):}`
What is the mean of the distribution?

Options

A. 3.76
B. 3.84
C. 3.96
D. 4.05

Explanation

To find the mean of the given frequency distribution, we will follow these steps:

### Step 1: Create a table for calculations
We will create a table that includes the number of calls (x), their corresponding frequencies (f), and the product of x and f (x * f).

| Number of Calls (x) | Frequency (f) | x * f |
|----------------------|---------------|-------|
| 0 | 14 | 0 |
| 1 | 21 | 21 |
| 2 | 25 | 50 |
| 3 | 43 | 129 |
| 4 | 51 | 204 |
| 5 | 40 | 200 |
| 6 | 39 | 234 |
| 7 | 12 | 84 |

### Step 2: Calculate the sum of frequencies (Σf)
Now we will calculate the total frequency (Σf):

\[ \Sigma f = 14 + 21 + 25 + 43 + 51 + 40 + 39 + 12 = 245 \]

### Step 3: Calculate the sum of x * f (Σ(x * f))
Next, we will calculate the total of the products (Σ(x * f)):

\[ \Sigma (x * f) = 0 + 21 + 50 + 129 + 204 + 200 + 234 + 84 = 922 \]

### Step 4: Calculate the mean
The mean (μ) of the distribution is calculated using the formula:

\[ \mu = \frac{\Sigma (x * f)}{\Sigma f} \]

Substituting the values we calculated:

\[ \mu = \frac{922}{245} \approx 3.76 \]

### Final Answer
Thus, the mean of the distribution is approximately **3.76**.

---