Find the mean of the following marks of 20 students on a screening test (out of 100). 76, 44, 45, 87, 71, 72, 82, 83, 41, 32, 75, 32, 46, 78, 17, 70, 84, 12, 77, 74

Options

A. 59.9
B. 51.5
C. 50
D. 25

Answer

To find the mean of the marks of 20 students, we will follow these steps:

### Step 1: List the Marks
The marks obtained by the 20 students are:
76, 44, 45, 87, 71, 72, 82, 83, 41, 32, 75, 32, 46, 78, 17, 70, 84, 12, 77, 74

### Step 2: Calculate the Sum of the Marks
We need to add all the marks together:
\[ 76 + 44 + 45 + 87 + 71 + 72 + 82 + 83 + 41 + 32 + 75 + 32 + 46 + 78 + 17 + 70 + 84 + 12 + 77 + 74 \]

Calculating this step-by-step:
- \(76 + 44 = 120\)
- \(120 + 45 = 165\)
- \(165 + 87 = 252\)
- \(252 + 71 = 323\)
- \(323 + 72 = 395\)
- \(395 + 82 = 477\)
- \(477 + 83 = 560\)
- \(560 + 41 = 601\)
- \(601 + 32 = 633\)
- \(633 + 75 = 708\)
- \(708 + 32 = 740\)
- \(740 + 46 = 786\)
- \(786 + 78 = 864\)
- \(864 + 17 = 881\)
- \(881 + 70 = 951\)
- \(951 + 84 = 1035\)
- \(1035 + 12 = 1047\)
- \(1047 + 77 = 1124\)
- \(1124 + 74 = 1198\)

So, the total sum of the marks is **1198**.

### Step 3: Count the Total Number of Students
The total number of students is given as **20**.

### Step 4: Calculate the Mean
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of Marks}}{\text{Total Number of Students}} = \frac{1198}{20} \]

Now, performing the division:
\[ 1198 \div 20 = 59.9 \]

### Final Answer
The mean of the marks is **59.9**.

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