A player timed 30 sleeper throws. Use the real dataset below to describe the data like a statistician. Show your work.
Dataset — sleeper times in seconds (30 throws):
1. Calculate the mean sleep time. (Add all 30 values, then divide by 30. Round to one decimal place.)
2. Find the median. Hint: sort the data smallest to largest first — with 30 values, average the 15th and 16th.
3. Find the mode — which sleep time occurred most often, and how many times?
4. Find the range of the dataset.
5. Spread: Two players each average a 25-second sleeper. Player A's throws range from 20–30 seconds; Player B's range from 5–45 seconds. Who is the more consistent player? What does Player B's wider spread tell you about their throws?
6. Outliers: Suppose one throw in the dataset had lasted 120 seconds instead of a typical value. Would the mean or the median change more? Which one better represents a "typical" throw in that case? Explain.
| 1. Mean ≈ 25.2 s (sum = 755; 755 ÷ 30 = 25.17) | 2. Median = 25.5 s (15th = 25, 16th = 26) |
| 3. Mode = 27 s (appears 3 times — more than any other value) | 4. Range = 29 s (41 − 12) |
5. Player A is more consistent. A wider spread means Player B's technique is less repeatable — some throws are much better and some much worse, so you can't predict the next throw well. 6. The mean would change more (one huge value pulls the average up noticeably); the median barely moves. The median better represents "typical" here because it resists outliers.