The mean of first three observations is 15 and the mean of next two observation is 20. The mean of all five observations is-

Options

A. 45
B. 15
C. 17
D. 40

Answer

To find the mean of all five observations, we can follow these steps:

### Step 1: Calculate the sum of the first three observations
We know that the mean of the first three observations is 15. The formula for the mean is:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

Let the first three observations be \(x_1, x_2, x_3\). Therefore, we have:

\[ \frac{x_1 + x_2 + x_3}{3} = 15 \]

Multiplying both sides by 3 gives us:

\[ x_1 + x_2 + x_3 = 3 \times 15 = 45 \]

### Step 2: Calculate the sum of the next two observations
We know that the mean of the next two observations is 20. Let these observations be \(x_4\) and \(x_5\). Thus, we have:

\[ \frac{x_4 + x_5}{2} = 20 \]

Multiplying both sides by 2 gives us:

\[ x_4 + x_5 = 2 \times 20 = 40 \]

### Step 3: Calculate the total sum of all five observations
Now, we can find the total sum of all five observations by adding the sums we calculated in Steps 1 and 2:

\[ x_1 + x_2 + x_3 + x_4 + x_5 = 45 + 40 = 85 \]

### Step 4: Calculate the mean of all five observations
Finally, we can find the mean of all five observations using the total sum:

\[ \text{Mean of all observations} = \frac{x_1 + x_2 + x_3 + x_4 + x_5}{5} = \frac{85}{5} = 17 \]

Thus, the mean of all five observations is **17**.

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