To calculate the mean, median, mode, and range for the data set: 22, 7, 22, 1, 7, 18, 18, 16, 6, 6, we will proceed step-by-step.
1. Mean
The mean is calculated by summing all the numbers and dividing by the count of the numbers.
Sum of the numbers: \[ 22 + 7 + 22 + 1 + 7 + 18 + 18 + 16 + 6 + 6 = 23 + 18 + 18 + 16 + 6 + 6 = 22 + 1 + 7 + 36 = 22 + 44 = 88 \]
Count of the numbers: 10
Mean: \[ \text{Mean} = \frac{88}{10} = 8.8 \]
2. Median
The median is the middle value when the numbers are arranged in ascending order.
Arranging the numbers in ascending order: \[ 1, 6, 6, 7, 7, 16, 18, 18, 22, 22 \]
Since there are 10 numbers (even), the median will be the average of the 5th and 6th values: 5th value: 7 6th value: 16
Median: \[ \text{Median} = \frac{7 + 16}{2} = \frac{23}{2} = 11.5 \]
3. Mode
The mode is the number that appears most frequently.
Counting the occurrences:
- 1: 1 time
- 6: 2 times
- 7: 2 times
- 16: 1 time
- 18: 2 times
- 22: 2 times
The mode is 6, 7, 18, and 22 because they all occur 2 times.
Mode: \[ \text{Mode} = 6, 7, 18, 22 \]
4. Range
The range is calculated by subtracting the smallest number from the largest number.
Smallest number: 1 Largest number: 22
Range: \[ \text{Range} = 22 - 1 = 21 \]
Summary:
- Mean = 8.8
- Median = 11.5
- Mode = 6, 7, 18, 22
- Range = 21
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