To calculate the mean, median, range, and midrange of the gallon sales data, let's first organize the data:
The gallons of paint sold each day are: 15, 20, 18, 22, 22, 28, 29
1. Mean
The mean is calculated by summing all the values and dividing by the number of values.
\[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{15 + 20 + 18 + 22 + 22 + 28 + 29}{7} = \frac{ 15 + 20 + 18 + 22 + 22 + 28 + 29 }{ 7 } \]
Calculating the sum: \[ 15 + 20 + 18 + 22 + 22 + 28 + 29 = 154 \]
Now divide by the number of days (7): \[ \text{Mean} = \frac{154}{7} = 22 \]
2. Median
The median is the middle number when the values are arranged in order. First, let's arrange the data: 15, 18, 20, 22, 22, 28, 29
The number of values is odd (7), so the median is the value at the 4th position: \[ \text{Median} = 22 \]
3. Range
The range is calculated by subtracting the smallest value from the largest value.
\[ \text{Range} = \text{Maximum} - \text{Minimum} = 29 - 15 = 14 \]
4. Midrange
The midrange is calculated by taking the average of the maximum and minimum values.
\[ \text{Midrange} = \frac{\text{Maximum} + \text{Minimum}}{2} = \frac{29 + 15}{2} = \frac{44}{2} = 22 \]
Summary
- Mean: 22
- Median: 22
- Range: 14
- Midrange: 22
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