Success Homeschool

Year 10 Mathematics · Comparing data distributions

Name: ______________________

Date: ____________

1. In a back-to-back stem-and-leaf plot, where are the stems?
- ☐ (a) On the left
- ☐ (b) In the middle, shared by both data sets
- ☐ (c) On the right
- ☐ (d) They are not used
2. Most values in a data set are low, with a long tail towards the high values. The distribution is:
- ☐ (a) negatively skewed
- ☐ (b) positively skewed
- ☐ (c) symmetric
- ☐ (d) bimodal
3. Which of these is a measure of spread?
- ☐ (a) Mean
- ☐ (b) Median
- ☐ (c) Range
- ☐ (d) Mode
4. A histogram has two separate peaks. Its shape is described as:
- ☐ (a) bimodal
- ☐ (b) symmetric
- ☐ (c) positively skewed
- ☐ (d) uniform
5. On the left side of a back-to-back stem-and-leaf plot, one row reads “8 5 2 | 4 |”. The key is 4 | 2 = 42. List the three values in order from smallest to largest.
6. Find the median of 12, 15, 15, 18, 20, 23, 31.
7. Find the range of 12, 15, 15, 18, 20, 23, 31.
8. Team A's points per game have a median of 24 and a range of 10. Team B's have a median of 24 and a range of 30. Which team scores more consistently? Answer A or B.

Answer sheet

1. In the middle, shared by both data sets — The stems sit in a central column, with one data set's leaves on each side.
2. positively skewed — A tail towards the high (positive) end is positive skew.
3. Range — The range (highest − lowest) measures spread. The others measure centre or the most common value.
4. bimodal — Two peaks (two modes) means bimodal.
5. 42, 45, 48 — Left-side leaves are read outwards from the stem: 2, 5, 8, giving 42, 45 and 48.
6. 18 — There are 7 values in order, so the median is the 4th value: 18.
7. 19 — 31 − 12 = 19.
8. A — The medians are equal, but Team A's range is much smaller, so its scores vary less.