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:
-
Sort the numbers:
8, 15, 16, 18, 21, 23, 23, 28 -
Mean:
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \] \[ = \frac{8 + 15 + 16 + 18 + 21 + 23 + 23 + 28}{8} = \frac{152}{8} = 19 \] -
Median:
Since there are 8 numbers (even count), the median will be the average of the 4th and 5th values in the sorted list.
\[ \text{Median} = \frac{18 + 21}{2} = \frac{39}{2} = 19.5 \] -
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).
\[ Q1 = \frac{15 + 16}{2} = \frac{31}{2} = 15.5 \] -
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
1 answer