In a community, 8 students were asked about the time they spend in watching T.V. during a week. They said 6 hrs, 8 hrs, 13 hrs, 9 hrs, 10 hrs, 5 hrs, 16 hrs and 3 hrs. Find the mean time devoted by them for watching T.V. during a week.

Options

A. 8 hrs 45 minutes
B. 6 hrs 10 minutes
C. 8 hrs 10 minutes
D. 6 hrs 45 minutes

Answer

To find the mean time devoted by the students for watching TV during a week, we can follow these steps:

### Step 1: List the Observations
The time spent by the 8 students watching TV is:
- 6 hrs
- 8 hrs
- 13 hrs
- 9 hrs
- 10 hrs
- 5 hrs
- 16 hrs
- 3 hrs

### Step 2: Count the Number of Observations
We have a total of 8 observations (students).

### Step 3: Calculate the Sum of Observations
Now, we need to sum all the hours spent watching TV:
\[ 6 + 8 + 13 + 9 + 10 + 5 + 16 + 3 \]

Calculating this step-by-step:
- \(6 + 8 = 14\)
- \(14 + 13 = 27\)
- \(27 + 9 = 36\)
- \(36 + 10 = 46\)
- \(46 + 5 = 51\)
- \(51 + 16 = 67\)
- \(67 + 3 = 70\)

So, the total sum of observations is **70 hours**.

### Step 4: Calculate the Mean
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} \]

Substituting the values we have:
\[ \text{Mean} = \frac{70}{8} \]

Calculating this gives:
\[ \text{Mean} = 8.75 \text{ hours} \]

### Step 5: Convert Decimal Hours to Hours and Minutes
The decimal part \(0.75\) hours can be converted to minutes:
\[ 0.75 \text{ hours} = 0.75 \times 60 \text{ minutes} = 45 \text{ minutes} \]

Thus, the mean time spent watching TV is:
\[ 8 \text{ hours } 45 \text{ minutes} \]

### Final Answer
The mean time devoted by the students for watching TV during a week is **8 hours 45 minutes**.

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