Comparing data sets with averages and range

Mathematics · Data & Statistics · ages 11-13

Name ______________________ Date ____________

In an ordered list of seven values, which measure uses the value with three observations on each side?
- Range of values
- Most common value
- Total divided by count
- Median
Six trays hold 11, 13, 11, 16, 11 and 13 seedlings. What is the mode?
- 13
- 16
- 11
- 12
A ribbon survey records four votes for striped, seven for plain and five for dotted. Which pattern is the mode?
- Striped
- Dotted
- No mode
- Plain
Five ribbons measure 24, 18, 27, 21 and 19 cm. What is the median length?
- 21
- 19
- 24
- 22
A data set is 10, 12, 12, 15, 21. What is the range?
Answer: ______________
Four jars weigh 18, 20, 22 and 24 grams. A fifth jar weighs 76 grams. What is the mean mass of all five jars?
Answer: ______________
Two classes take the same quiz. Class A has a mean score of 78. Class B has a mean score of 71 and a much smaller range. Here, compare consistency using range. What can you say?
- Class B was more consistent
- Class A definitely has no outliers
- Class B has a higher mode than Class A
Package masses in grams are A: 12, 14, 14, 16, 19 and B: 9, 11, 14, 20, 26. Which conclusion follows from their medians and ranges?
- Same median; A has the smaller range
- B has the smaller range because its smallest mass is lower
- A has the higher median because its smallest mass is higher
- Both ranges are equal because both groups contain five packages
Sam wants a typical value for 3, 3, 4, 5, 100. He says, 'The mean is way bigger than the median, so I should trust the mean more because it uses all the numbers.' What is wrong with his reasoning?
- Sam is right, the mean is always the best measure
- The median cannot be calculated when there is an outlier
- The outlier skews the mean, so trust the median here
Bag A holds marbles weighing 5, 5, 6, 8, 46 grams. Bag B holds marbles weighing 5, 6, 6, 7, 8 grams. Both bags have the same median weight. How many grams bigger is Bag A's range than Bag B's range?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

Comparing data sets with averages and range W1-mt_XSXnTQoQ4l-s1

Median · The described value occupies the middle position. With an odd count, the median is the value in that position.
11 · 11 occurs three times, 13 twice and 16 once. The most frequent value is 11, so the mode is 11.
Plain · Plain received seven votes, the largest count. The mode is the pattern plain, not the number seven.
21 · In order, the lengths are 18, 19, 21, 24 and 27 cm. The third value is 21, with two values on each side.
11 · The range is the biggest number minus the smallest: 21 minus 10 equals 11.
32 · The first four masses total 84 grams. Adding 76 gives 160 grams across five jars, so the new mean is 160 / 5 = 32 grams.
Class B was more consistent · Class B has the smaller range, so its smallest and largest scores are closer together. By the question's range-based comparison, Class B was more consistent. Its mean score of 71 is lower than Class A's 78.
Same median; A has the smaller range · Both ordered lists have middle value 14. A's range is 19 - 12 = 7; B's is 26 - 9 = 17. Their medians match, but A has the smaller range.
The outlier skews the mean, so trust the median here · The outlier 100 raises the mean to 23, above the other four values. The median is 4, among those four values. For Sam's goal of describing a typical value, the median is more suitable here; using every value does not make the mean best for every purpose.
38 · Bag A's range is 46 minus 5, which is 41. Bag B's range is 8 minus 5, which is 3. The difference is 41 minus 3, which is 38: Bag A's outlier makes its range much bigger even though the medians match.