Describing Distribution Shape - Pre Algebra
- In a town, most homes sell for moderate prices, but a few sell for very high prices. In which direction is the distribution of prices skewed?
- Skewed right. The few very high prices form a long tail toward the higher values.
- What is a cluster in a distribution?
- A group of data values that are bunched close together.
- Most quiz scores fall between 8 and 10, with a few low scores stretching down to 2. In which direction is the distribution skewed?
- Skewed left. The long tail extends toward the lower values.
- What does it mean for a distribution to be skewed right?
- It has a long tail extending toward the higher values on the right, with most data on the left.
- What is an outlier in a data set?
- A value that is much greater or much less than the rest of the data.
- A dot plot shows the values 1, 1, 2, 2, 2, 8, 9, 9. Where is the gap?
- Between 2 and 8. No data values fall from 3 through 7.
- Which value is an outlier in the data set 2, 3, 3, 4, 4, 4, 5, 30?
- 30. It lies far above all the other values, which are between 2 and 5.
- What is a peak in a distribution?
- A value or interval where the data are most concentrated. A distribution with two peaks is called bimodal.
- In a distribution that is strongly skewed right, how does the mean usually compare to the median?
- The mean is usually greater than the median, because the long right tail pulls the mean toward the higher values.
- What does it mean for a distribution to be skewed left?
- It has a long tail extending toward the lower values on the left, with most data on the right.
- What is a gap in a distribution?
- An interval of the scale that contains no data values.
- What does it mean for a distribution to be symmetric?
- Its left and right halves are roughly mirror images around the center.