Find the mean of the following data :
30,32,24,34, 26,28, 30, 35, 33, 25
Find the median of the given data.

Answer

To find the mean and median of the given data set: 30, 32, 24, 34, 26, 28, 30, 35, 33, 25, follow these steps:

### Step 1: Calculate the Mean
1. **Sum the Observations**:
Add all the numbers in the data set.
\[ 30 + 32 + 24 + 34 + 26 + 28 + 30 + 35 + 33 + 25 \]
Performing the addition:
\[ = 30 + 32 = 62 \\ = 62 + 24 = 86 \\ = 86 + 34 = 120 \\ = 120 + 26 = 146 \\ = 146 + 28 = 174 \\ = 174 + 30 = 204 \\ = 204 + 35 = 239 \\ = 239 + 33 = 272 \\ = 272 + 25 = 297 \]
So, the sum of the observations is **297**.

2. **Count the Number of Observations**:
There are 10 numbers in the data set.

3. **Calculate the Mean**:
Divide the sum by the total number of observations.
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{297}{10} = 29.7 \]

### Step 2: Calculate the Median
1. **Arrange the Data in Ascending Order**:
The sorted data set is:
\[ 24, 25, 26, 28, 30, 30, 32, 33, 34, 35 \]

2. **Determine the Number of Observations**:
The number of observations (n) is 10, which is even.

3. **Find the Median**:
For an even number of observations, the median is the average of the two middle numbers.
- The middle positions are \( n/2 \) and \( n/2 + 1 \), which are the 5th and 6th terms.
- The 5th term is 30 and the 6th term is also 30.
\[ \text{Median} = \frac{\text{5th term} + \text{6th term}}{2} = \frac{30 + 30}{2} = \frac{60}{2} = 30 \]

### Final Answers:
- **Mean**: 29.7
- **Median**: 30

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