Sure! Let's go through the process of calculating the range, median, and mode for the given data set step-by-step. The data set is: 35, 32, 35, 42, 38, 32, 34.
### 1. Finding the Range
The range is the difference between the maximum and minimum values in the data set.
- First, identify the maximum and minimum values:
- Maximum value: 42
- Minimum value: 32
- Range = Maximum value - Minimum value
- Range = 42 - 32 = 10
So, the range of the data set is 10.
### 2. Finding the Median
The median is the middle number when the data set is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers.
1. First, sort the data set in ascending order:
- Sorted data set: 32, 32, 34, 35, 35, 38, 42
2. Determine the number of observations in the data set:
- Number of observations = 7 (which is odd)
3. Since the number of observations is odd, the median is the middle number:
- Middle number (7th observation) is at position (7 + 1) / 2 = 4
- Median = 35
So, the median of the data set is 35.
### 3. Finding the Mode
The mode is the number that appears most frequently in the data set.
1. Look for the number(s) that appear most frequently:
- 32 appears 2 times
- 35 appears 2 times
- Other numbers appear only once
2. Among the numbers that appear most frequently, considering the mode by definition:
- Mode = 32 (It appears more frequently among the duplicated values in dataset)
So, the mode of the data set is 32.
### Summary
- Range: 10
- Median: 35
- Mode: 32
These calculations provide a comprehensive understanding of the variability, central tendency, and frequency of the data set.
