Sure! Let's go through each of the statistical measures step-by-step: median, mean, range, and interquartile range (IQR).
1. Median:
The median is the middle value of an ordered dataset.
- First, list the data in ascending order: [0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 9]
- Since there are 12 data points, the median is the average of the 6th and 7th values: (2 + 3) / 2 = 2.5
2. Mean:
The mean is the average of all data points.
- Sum all the data points: 0 + 5 + 6 + 0 + 2 + 3 + 3 + 4 + 1 + 9 + 2 + 1 = 36
- Divide by the number of data points: 36 / 12 = 3.0
3. Range:
The range is the difference between the maximum and minimum values.
- Maximum value: 9
- Minimum value: 0
- Range: 9 - 0 = 9
4. Interquartile Range (IQR):
The IQR is the difference between the first quartile (Q1) and the third quartile (Q3).
- Q1 is the 25th percentile. It is the value at 1/4th of the ordered dataset.
- Q3 is the 75th percentile. It is the value at 3/4th of the ordered dataset.
- For the dataset [0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 9]:
- Q1 (25th percentile): The average of the 3rd and 4th values: (1 + 1) / 2 = 1
- Q3 (75th percentile): The average of the 9th and 10th values: (4 + 5) / 2 = 4.5
- IQR: Q3 - Q1 = 4.5 - 1 = 3.25
So, our final results are:
- Median: 2.5
- Mean: 3.0
- Range: 9
- IQR: 3.25
These calculations help us understand the central tendency, spread, and dispersion of the given dataset.
