Question

22, 7, 22, 1, 7, 18, 18, 16, 6, 6 mean = _____ median = _____ mode = _____ range = _____

Answer 1

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