Durations of sunshine (in hours) in Amritsar for first 10 days of August 1997 as reported by the Meteorological Department are given below. 9.6, 5.2, 3.5, 1.5, 1.6, 2.4, 2.6, 8.4, 10.3, 10.9
Find the mean.

Options

A. 5.4
B. 3.6
C. 5.6
D. 6.5

Answer

To find the mean duration of sunshine in Amritsar for the first 10 days of August 1997, we will follow these steps:

### Step 1: List the Data
The durations of sunshine (in hours) for the first 10 days are:
- 9.6
- 5.2
- 3.5
- 1.5
- 1.6
- 2.4
- 2.6
- 8.4
- 10.3
- 10.9

### Step 2: Calculate the Sum of the Data
We need to sum all the values:
\[ \text{Sum} = 9.6 + 5.2 + 3.5 + 1.5 + 1.6 + 2.4 + 2.6 + 8.4 + 10.3 + 10.9 \]

Calculating this step-by-step:
- \(9.6 + 5.2 = 14.8\)
- \(14.8 + 3.5 = 18.3\)
- \(18.3 + 1.5 = 19.8\)
- \(19.8 + 1.6 = 21.4\)
- \(21.4 + 2.4 = 23.8\)
- \(23.8 + 2.6 = 26.4\)
- \(26.4 + 8.4 = 34.8\)
- \(34.8 + 10.3 = 45.1\)
- \(45.1 + 10.9 = 56.0\)

So, the total sum of the durations is:
\[ \text{Sum} = 56.0 \]

### Step 3: Count the Number of Observations
The total number of observations (days) is:
\[ \text{Number of observations} = 10 \]

### Step 4: Calculate the Mean
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{56.0}{10} \]
Calculating this gives:
\[ \text{Mean} = 5.6 \]

### Final Answer
Thus, the mean duration of sunshine in Amritsar for the first 10 days of August 1997 is:
\[ \text{Mean} = 5.6 \text{ hours} \]

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