The scores (out of 25) of 9 students in a Monday test are 14, 25, 17, 22, 20, 19, 10, 8 and 23. Find the sum of mean score and median score of the data.

Options

A. 35
B. 35.5
C. 36.56
D. 36

Answer

To solve the problem, we need to find the sum of the mean score and the median score of the given data. Here are the steps to achieve that:

### Step 1: Calculate the Mean Score
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \]

**Calculating the sum of scores:**
The scores of the 9 students are: 14, 25, 17, 22, 20, 19, 10, 8, and 23.

Sum of scores:
\[ 14 + 25 + 17 + 22 + 20 + 19 + 10 + 8 + 23 = 14 + 25 = 39 \]
\[ 39 + 17 = 56 \]
\[ 56 + 22 = 78 \]
\[ 78 + 20 = 98 \]
\[ 98 + 19 = 117 \]
\[ 117 + 10 = 127 \]
\[ 127 + 8 = 135 \]
\[ 135 + 23 = 158 \]

So, the total sum of scores is **158**.

**Total number of observations:**
There are 9 students, so the total number of observations is **9**.

**Calculating the mean:**
\[ \text{Mean} = \frac{158}{9} \approx 17.56 \text{ (rounded to two decimal places)} \]

### Step 2: Calculate the Median Score
To find the median, we first need to arrange the scores in ascending order:
\[ 8, 10, 14, 17, 19, 20, 22, 23, 25 \]

Since there are 9 observations (an odd number), the median is the middle value. The middle value can be found using the formula:
\[ \text{Median} = \text{Value at position} \left(\frac{n + 1}{2}\right) \]
Where \( n \) is the total number of observations.

**Finding the position:**
\[ \frac{9 + 1}{2} = 5 \]
The 5th term in the ordered list is **19**.

### Step 3: Calculate the Sum of Mean and Median
Now, we add the mean and median:
\[ \text{Sum} = \text{Mean} + \text{Median} = 17.56 + 19 = 36.56 \]

### Final Answer
The sum of the mean score and the median score is **36.56**.

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