Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if each of the observations, given above, be :
divided by 2.

Answer

To find the mean of the numbers 8, 12, 16, 22, 10, and 4, and then determine the resulting mean after dividing each observation by 2, we can follow these steps:

### Step 1: Calculate the sum of the observations.
Add all the numbers together:
\[ 8 + 12 + 16 + 22 + 10 + 4 \]

### Step 2: Perform the addition.
Calculating the sum:
\[ 8 + 12 = 20 \\ 20 + 16 = 36 \\ 36 + 22 = 58 \\ 58 + 10 = 68 \\ 68 + 4 = 72 \]
So, the total sum is 72.

### Step 3: Count the number of observations.
There are 6 observations in total: 8, 12, 16, 22, 10, and 4.

### Step 4: Calculate the mean.
The mean is calculated by dividing the sum of the observations by the number of observations:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{72}{6} \]

### Step 5: Perform the division.
Calculating the mean:
\[ \frac{72}{6} = 12 \]
Thus, the mean of the original observations is 12.

### Step 6: Find the new mean after dividing each observation by 2.
If each observation is divided by 2, the new mean can be calculated as:
\[ \text{New Mean} = \frac{\text{Old Mean}}{2} = \frac{12}{2} \]

### Step 7: Perform the division for the new mean.
Calculating the new mean:
\[ \frac{12}{2} = 6 \]
Thus, the resulting mean after dividing each observation by 2 is 6.

### Final Answer:
The mean of the observations is 12, and the resulting mean after dividing each observation by 2 is 6.

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