First, determine the range of the data without the outlier.
Then, determine the range of the data with the outlier.
Finally, make a conclusion about the effect of an outlier on range.
How Much Did It Rain Last Spring?
A number line labeled number of days each week ranges from 0 to 7 in increments of 1. It is titled how much did it rain last spring? Data are: 0, 1; 3, 3; 4, 3; 5, 3; 6, 2; 7, 1.
Number of Days Each Week
CLEAR CHECK
The range without the outlier is days.
The range with the outlier is days.
When we add an outlier, the range will never , but it may .
The range without the outlier is 7 - 0 = 7 days. (Note: The range is calculated by subtracting the smallest value from the largest value.)
The range with the outlier is 7 - 0 = 7 days as well. The outlier value does not affect the range since it is within the same range as the other data points.
Conclusion: In this case, the outlier does not affect the range. The presence of an outlier may or may not have an effect on the range, depending on its position relative to the rest of the data values.
To determine the range without the outlier, we need to calculate the difference between the smallest and the largest value in the data set. Without the outlier, the data set is 0, 1; 3, 3; 4, 3; 5, 3; 6, 2; 7, 1. The smallest value is 0 and the largest value is 7. Therefore, the range without the outlier is 7 - 0 = 7 days.
To determine the range with the outlier, we need to include the outlier value. In this case, the outlier is not specified, so we cannot calculate the exact range with the outlier.
However, we can discuss the effect of an outlier on the range. An outlier is a value that significantly differs from the other values in the data set. When we add an outlier, the range will never decrease, but it may increase depending on the value of the outlier. If the outlier is larger than the largest value in the data set, the range will increase. If the outlier is smaller than the smallest value in the data set, the range will also increase.
To determine the range of the data without the outlier, we need to arrange the data points in ascending order:
0, 1, 3, 3, 4, 3, 5, 3, 6, 2, 7, 1
The lowest value is 0 and the highest value is 7. Therefore, the range without the outlier is 7 - 0 = 7 days.
Now let's determine the range of the data with the outlier. Since there is no mention of which value is the outlier, we'll assume that it is the highest value, which is 7.
Without the outlier, the range was 7 days. With the outlier included, the range is still 7 days. Therefore, the range does not change when the outlier is included.
In conclusion, adding an outlier to a data set may or may not affect the range. In this case, including the outlier did not change the range.