Range Outliers Quiz: Range and the Effect of Outliers

An outlier is a value that is much larger or much smaller than most other values in a data set. In this set, the values 4, 5, 6, and 7 are all close together, but 50 is far away from the rest. The large gap between 50 and the nearest value of 7 is what makes 50 stand out as the outlier. An outlier is not simply the largest or smallest value — it must be significantly separated from the rest of the data.

The answer is False. An outlier typically makes the range larger, not smaller. Because the range is found by subtracting the smallest value from the largest, a very high or very low outlier becomes one of those extremes and widens the gap between them. Removing an outlier usually decreases the range. A data set with an outlier almost always has a larger range than the same data set without it.

The range is found by subtracting the smallest value from the largest. The smallest value is 3 and the largest is 40. Subtracting gives 40 minus 3, which equals 37. The value 40 is far from the rest of the data and is an outlier. Because it is the largest value, it directly determines the upper end of the range and causes the range to be much larger than it would be without it.

Without the outlier 80, the remaining values are 10, 11, 12, 12, and 13. The new largest value is 13 and the smallest is 10. Subtracting gives 13 minus 10, which equals 3. Before removing 80, the range was 80 minus 10, which equals 70. Removing the outlier reduced the range from 70 all the way down to 3, showing how much a single outlier can inflate the range of a data set.

In option C, the values 5, 6, 6, and 7 are all close together, but 50 is far away from the rest. The large gap between 50 and the next highest value of 7 makes 50 an outlier. In the other options, all values are close to each other with no large gaps, so none of those sets contain an outlier. An outlier is identified by a significant separation between it and the rest of the data.

The answer is True. An outlier sits far from the rest of the data and typically becomes either the highest or lowest value in the set. Since the range depends on the highest and lowest values, removing the outlier removes one of those extremes. This either reduces the range or, in rare cases where the next value is equally extreme, keeps it the same. The range cannot increase simply by removing a value from the set.

When 45 is removed, the remaining values are 2, 3, 3, 4, 4, and 5. The new largest value is 5 and the smallest is 2. Subtracting gives 5 minus 2, which equals 3. The range drops from 43 down to 3 because 45 was the outlier driving the range upward. This shows how a single outlier can make the range far larger than it would be if only the typical values were present.

The range is 35 minus 1, which equals 34, making option A true. The value 35 is far from the other values, which all sit between 1 and 4, making it an outlier, so option B is true. Removing 35 leaves 4 as the new largest and 1 as the smallest, giving a new range of 3, making option D true. Option C is false because removing an outlier decreases the range, not increases it.

An outlier sits far from the rest of the data and typically becomes either the highest or lowest value in the set. Since the range is calculated using only those two extreme values, the outlier directly determines one end of the range calculation. This causes the gap between the highest and lowest to be much larger than it would be if the outlier were not present, inflating the range significantly.

The answer is True. The range is calculated by subtracting only the smallest value from the largest value. Any value that falls between those two extremes plays no role in the calculation. For example, in the set 5, 20, 35, changing the middle value of 20 to any number between 5 and 35 does not change the range at all, because the highest value remains 35 and the lowest remains 5.

The range is 100 minus 6, which equals 94. The values 6 through 9 all cluster closely together, but 100 is far away from the rest of the group, making it the outlier. Because 100 is the largest value, it determines the upper end of the range and is directly responsible for the range being as large as it is. Without 100, the range would only be 9 minus 6, which equals 3.

Being the smallest value does not automatically make a number an outlier. An outlier must be significantly far from the rest of the data. In this set, all values are evenly spaced and close together, with each number only 1 apart from the next. There is no large gap between 5 and the other values, so it is not an outlier. Outliers are identified by a dramatic separation, not simply by being the lowest or highest number in the set.

The range is 20 minus 1, which equals 19. The values 15 through 20 all cluster closely together, but 1 is far away from the rest of the group, making it the outlier. This is an example of a low outlier — a value that is unusually small compared to the rest of the data. The low outlier becomes the minimum and directly pulls the bottom of the range downward.

The range is 60 minus 4, which equals 56, making option A true. The value 60 is far from the other values which all sit between 4 and 7, making it an outlier, so option C is true. Removing 60 leaves 7 as the new largest and 4 as the smallest, giving 7 minus 4 equals 3, making option D true. Option B is false because removing an outlier decreases the range, not increases it.

The answer is False. When values are arranged in order from smallest to largest, an outlier always appears at one of the ends — either as the smallest value or the largest value. It cannot sit in the middle because the middle values are the ones closest to the rest of the data. An outlier is defined by being far from the group, which places it at the extreme low or high end of the ordered set.

The range before removing 75 is 75 minus 8, which equals 67. After removing 75, the remaining values are 8, 9, 10, 10, 11, and 12. The new largest value is 12 and the smallest is still 8. Subtracting gives 12 minus 8, which equals 4. The range drops from 67 to 4, clearly showing how dramatically a single outlier can inflate the range of a data set.

The range is found using only the highest and lowest values in a set. An outlier, being far from the rest of the data, typically becomes either the maximum or the minimum. This means the outlier directly controls one end of the range calculation, making the range much larger than it would be without it. The values in the middle of the set have no impact on the range regardless of how many there are.

The range is 90 minus 3, which equals 87. If 90 is removed, the remaining values are 3, 3, 4, 4, 5, and 5. The new largest is 5 and the smallest is still 3. Subtracting gives 5 minus 3, which equals 2. The range shrinks from 87 to 2, showing how much the outlier 90 was driving the range upward. This is a clear example of how one extreme value can dominate the range of a data set.

The answer is False. The range is found by subtracting the smallest value from the largest, so it is a difference between two values, not the outlier itself. For example, in the set 2, 3, 4, 5, 50, the outlier is 50 but the range is 50 minus 2, which equals 48. The range and the outlier value are almost never the same number. The outlier influences the size of the range but is not equal to it.

The mean is calculated by adding all values and dividing by the count, which involves every number in the set. The range, on the other hand, only uses the highest and lowest values. This means two classes can have scores that average to the same mean while having very different gaps between their extreme scores. A large range means scores are spread widely, while a small range means they are clustered closely, and neither one determines the other.