The mean of a set of 120 observations is 80. 10 is subtracted from each observation and each of the corresponding result is divided by 7. What is the mean of the new set?

Options

A. 7
B. 10
C. `5(5)/6`
D. `7(1)/12`

Answer

To solve the problem step by step, we will follow the mathematical operations described in the question.

### Step 1: Calculate the sum of the original observations
Given that the mean of the original set of observations is 80 and there are 120 observations, we can calculate the total sum of the original observations using the formula:

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

Substituting the values:

\[ \text{Sum of observations} = 80 \times 120 = 9600 \]

### Step 2: Subtract 10 from each observation
Next, we subtract 10 from each of the 120 observations. This will reduce the total sum of the observations:

\[ \text{New sum} = \text{Original sum} - (10 \times \text{Number of observations}) \]

Calculating this:

\[ \text{New sum} = 9600 - (10 \times 120) = 9600 - 1200 = 8400 \]

### Step 3: Divide each observation by 7
Now, we need to find the mean of the new set after dividing each observation by 7. The mean of the new set can be calculated as:

\[ \text{New mean} = \frac{\text{New sum}}{7 \times \text{Number of observations}} \]

Calculating this:

\[ \text{New mean} = \frac{8400}{7 \times 120} \]

Calculating the denominator:

\[ 7 \times 120 = 840 \]

Thus, we have:

\[ \text{New mean} = \frac{8400}{840} = 10 \]

### Final Answer
The mean of the new set is **10**.

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