The mean of first three items is 14 and mean of next two items is 18. The mean of all the five terms is :

Options

A. 14.5
B. `15.0`
C. 15.2
D. 15.6

Answer

To find the mean of all five terms given the means of the first three and the next two terms, we can follow these steps:

### Step 1: Identify the given values
- Mean of the first three items (m1) = 14
- Number of first three items (x1) = 3
- Mean of the next two items (m2) = 18
- Number of next two items (x2) = 2

### Step 2: Calculate the total sum of the first three items
To find the total sum of the first three items, we can use the formula:
\[ \text{Total sum of first three items} = \text{Mean} \times \text{Number of items} = m1 \times x1 \]
Substituting the values:
\[ \text{Total sum of first three items} = 14 \times 3 = 42 \]

### Step 3: Calculate the total sum of the next two items
Similarly, for the next two items:
\[ \text{Total sum of next two items} = m2 \times x2 \]
Substituting the values:
\[ \text{Total sum of next two items} = 18 \times 2 = 36 \]

### Step 4: Calculate the total sum of all five items
Now, we can find the total sum of all five items by adding the sums from the previous steps:
\[ \text{Total sum of all five items} = \text{Total sum of first three items} + \text{Total sum of next two items} \]
Substituting the values:
\[ \text{Total sum of all five items} = 42 + 36 = 78 \]

### Step 5: Calculate the mean of all five items
Finally, we can find the mean of all five items using the formula:
\[ \text{Mean of all five items} = \frac{\text{Total sum of all five items}}{\text{Total number of items}} = \frac{78}{5} \]
Calculating this gives:
\[ \text{Mean of all five items} = 15.6 \]

### Final Answer:
The mean of all five terms is **15.6**.

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