Question

out of these number, 23, 21, 18, 23, 28, 15, 8, 16
what is the mean,median, 1st quartile and 3rd

Answer 1

To calculate the mean, median, and quartiles (1st and 3rd) for the given set of numbers (23, 21, 18, 23, 28, 15, 8, 16), follow these steps:

1. **Sort the numbers**:
8, 15, 16, 18, 21, 23, 23, 28

2. **Mean**:
\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
\]
\[
= \frac{8 + 15 + 16 + 18 + 21 + 23 + 23 + 28}{8} = \frac{152}{8} = 19
\]

3. **Median**:
Since there are 8 numbers (even count), the median will be the average of the 4th and 5th values in the sorted list.
\[
\text{Median} = \frac{18 + 21}{2} = \frac{39}{2} = 19.5
\]

4. **1st Quartile (Q1)**:
The 1st quartile is the median of the first half of the data (which includes the first 4 sorted numbers):
8, 15, 16, 18 (the median here is between the 2nd and 3rd values).
\[
Q1 = \frac{15 + 16}{2} = \frac{31}{2} = 15.5
\]

5. **3rd Quartile (Q3)**:
The 3rd quartile is the median of the second half of the data (which includes the last 4 sorted numbers):
21, 23, 23, 28 (the median here is between the 2nd and 3rd values).
\[
Q3 = \frac{23 + 23}{2} = \frac{46}{2} = 23
\]

### Summary of calculations:
- **Mean**: 19
- **Median**: 19.5
- **1st Quartile (Q1)**: 15.5
- **3rd Quartile (Q3)**: 23