Data Day
Data Day: Center and Spread at Home
Rocket digs out last Saturday's tally sheet. "Reading minutes. 20, 20, 30, 15, 35. Now I can give it a center!"
"Two centers," Raven says. "What do you notice when you find both?"
Rocket adds. "120 divided by 5 is 24. That is the mean." He orders them. "15, 20, 20, 30, 35. The median is 20."
"They disagree," Nova says. "What is the shape telling you?"
"Two people at 20 and a long tail up to 35," Rocket says. "The tail pulls the mean up."
"And the spread?" Raven asks.
"Range 20," Rocket says. "From 15 to 35."
Nova dims. "Now you can describe your family in three numbers. Go collect a new set."
- The mean is the fair share: add everything and divide by the count.
- The median is the middle value in order. It resists far out values.
- The range, the MAD and the IQR each measure spread with one number.
- Balanced data: report the mean and the MAD. Lopsided data: report the median and the IQR.
- Compare two groups by the gap between their centers, measured in MADs.
Rocket's family data, one week on
Last week's five answers were 20, 20, 30, 15, 35 minutes. In order: 15, 20, 20, 30, 35.
Mean: 120 ÷ 5 = 24. Median: 20. Range: 35 - 15 = 20.
The mean is higher than the median because the data has a tail toward the high values. The median fits this shape better.
Write every number, never who gave it. Put each set in order.
Find the mean, the median and the range of each set together. Say which center fits the shape.
If you have two people's toss sets, compare their means. Whose tosses spread wider?
Survey questions stay about things like minutes, steps or tosses. They never record names or ages.
Decimals are fine in a mean. If your student gets 137.5, that is a correct answer, not a mistake.
- Read the question.
- Tap your answer.
What is the mean of Rocket's family reading minutes?What is the median of Rocket's family reading minutes?A full week of centers and spreads. Next week you add chance to the mix and run the Data Fair.