Answer :
We are given the monthly rainfall amounts:
[tex]$$7.6,\; 6.7,\; 8.1,\; 6.2,\; 6.0,\; 6.2.$$[/tex]
Below is a step-by-step explanation to determine the mean, median, mode, and range.
1. Mean:
To calculate the mean, add all the values together and divide by the number of values.
[tex]$$\text{Mean} = \frac{7.6 + 6.7 + 8.1 + 6.2 + 6.0 + 6.2}{6}.$$[/tex]
First, add the values:
[tex]$$7.6 + 6.7 = 14.3,$$[/tex]
[tex]$$14.3 + 8.1 = 22.4,$$[/tex]
[tex]$$22.4 + 6.2 = 28.6,$$[/tex]
[tex]$$28.6 + 6.0 = 34.6,$$[/tex]
[tex]$$34.6 + 6.2 = 40.8.$$[/tex]
Then, divide by 6:
[tex]$$\text{Mean} = \frac{40.8}{6} = 6.8.$$[/tex]
Therefore, the mean monthly rainfall is [tex]$6.8$[/tex] inches.
2. Median:
The median is the middle value when the data set is arranged in order. First, sort the data:
[tex]$$6.0,\; 6.2,\; 6.2,\; 6.7,\; 7.6,\; 8.1.$$[/tex]
Since there are 6 values (an even number), the median is the average of the third and fourth values:
[tex]$$\text{Median} = \frac{6.2 + 6.7}{2} = \frac{12.9}{2} = 6.45.$$[/tex]
So, the median monthly rainfall is [tex]$6.45$[/tex] inches.
3. Mode:
The mode is the value that appears most frequently. In the data set, [tex]$6.2$[/tex] occurs twice while all other values occur only once.
Therefore, the mode is [tex]$6.2$[/tex] inches.
4. Range:
The range is the difference between the maximum and minimum values.
- The maximum value is [tex]$8.1$[/tex] inches.
- The minimum value is [tex]$6.0$[/tex] inches.
Thus,
[tex]$$\text{Range} = 8.1 - 6.0 = 2.1.$$[/tex]
The range of the data set is [tex]$2.1$[/tex] inches.
To fill in the blank for the mean monthly rainfall:
[tex]$$\boxed{6.8\ \text{inches}}.$$[/tex]
[tex]$$7.6,\; 6.7,\; 8.1,\; 6.2,\; 6.0,\; 6.2.$$[/tex]
Below is a step-by-step explanation to determine the mean, median, mode, and range.
1. Mean:
To calculate the mean, add all the values together and divide by the number of values.
[tex]$$\text{Mean} = \frac{7.6 + 6.7 + 8.1 + 6.2 + 6.0 + 6.2}{6}.$$[/tex]
First, add the values:
[tex]$$7.6 + 6.7 = 14.3,$$[/tex]
[tex]$$14.3 + 8.1 = 22.4,$$[/tex]
[tex]$$22.4 + 6.2 = 28.6,$$[/tex]
[tex]$$28.6 + 6.0 = 34.6,$$[/tex]
[tex]$$34.6 + 6.2 = 40.8.$$[/tex]
Then, divide by 6:
[tex]$$\text{Mean} = \frac{40.8}{6} = 6.8.$$[/tex]
Therefore, the mean monthly rainfall is [tex]$6.8$[/tex] inches.
2. Median:
The median is the middle value when the data set is arranged in order. First, sort the data:
[tex]$$6.0,\; 6.2,\; 6.2,\; 6.7,\; 7.6,\; 8.1.$$[/tex]
Since there are 6 values (an even number), the median is the average of the third and fourth values:
[tex]$$\text{Median} = \frac{6.2 + 6.7}{2} = \frac{12.9}{2} = 6.45.$$[/tex]
So, the median monthly rainfall is [tex]$6.45$[/tex] inches.
3. Mode:
The mode is the value that appears most frequently. In the data set, [tex]$6.2$[/tex] occurs twice while all other values occur only once.
Therefore, the mode is [tex]$6.2$[/tex] inches.
4. Range:
The range is the difference between the maximum and minimum values.
- The maximum value is [tex]$8.1$[/tex] inches.
- The minimum value is [tex]$6.0$[/tex] inches.
Thus,
[tex]$$\text{Range} = 8.1 - 6.0 = 2.1.$$[/tex]
The range of the data set is [tex]$2.1$[/tex] inches.
To fill in the blank for the mean monthly rainfall:
[tex]$$\boxed{6.8\ \text{inches}}.$$[/tex]
