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Ratios and Data 6-8 / Week 11 / Monday
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Week 11 · Center and Spread

Monday

One number for the middle
// One number for the middle, one number for the scatter
⏱ about 20 min

Monday: One Number for the Middle

Rocket dumps a pile of beans onto the Numbers Desk. "Beanbag toss practice. Raven scored 6, 8, 5, 9, 8, 7 and 6."

"Seven throws, seven scores," Raven says. "If someone asks how I did, I cannot read them all seven numbers."

"Then give them one number," Nova says, hovering over the beans. "Which one?"

Rocket sorts the beans into seven piles, one per throw. "The piles are all different heights."

"What do you notice if you share them out evenly?" Raven asks.

Rocket slides beans from the tall piles to the short ones. "Seven beans in every pile. Seven is her fair share."

"That fair share has a name," Nova says. "And there is a second way to find a middle."

Rocket lines the scores up in order. "5, 6, 6, 7, 8, 8, 9. The middle one is 7 too!"

Rocket, Raven and Nova at the Numbers Desk with seven piles of beans, a line of beanbags and a score sheet.

The mean: a fair share

A measure of center sums up a whole data set with a single number. It answers the question "What is typical here?"

The mean is the fair share. Add every value, then divide by how many values there are.

Raven's scores add to 49. There are 7 throws. 49 ÷ 7 = 7.

Rocket's bean piles show why. Leveling the piles moves beans from high scores to low ones until every pile matches. That level is the mean.

The median: the middle value

The median is the value in the middle when the data is in order. Half the values sit below it and half above.

In order, Raven's scores are 5, 6, 6, 7, 8, 8, 9. The middle value, the fourth of seven, is 7.

With an even number of values there are two middle values. The median is the mean of those two.

Rocket's five scores were 4, 9, 6, 5, 6. In order: 4, 5, 6, 6, 9. The median is 6, and the mean is 30 ÷ 5 = 6.

For both crew members the mean and the median agree. That happens when the data is balanced. It does not always happen.

A dot plot of Raven's toss points from 5 to 9, balanced around 7.
MeasureHow to find itRaven's scores
MeanAdd all values, divide by the count49 ÷ 7 = 7
MedianOrder the values, take the middle one5, 6, 6, 7, 8, 8, 9 gives 7
FIND THE CENTER
  • Read the question.
  • Tap your answer.
A dot plot of Raven's toss pointsWhat is the mean of Raven's seven toss scores?
A dot plot of Rocket's toss pointsWhat is the median of Rocket's scores: 4, 9, 6, 5, 6?
What is the mean of Rocket's scores: 4, 9, 6, 5, 6?
Rocket's second round was 3, 9, 9, 10, 9. What is the median?
MEAN OR MEDIAN?
  • Read the question.
  • Tap your answer.
Which measure of center is found by adding every value and dividing by the count?
Which measure of center is the middle value once the data is in order?
Rocket's second round was 3, 9, 9, 10, 9. What is the mean?
How many throws did Raven make in practice? Type the number.
WHY THIS EXERCISEThe count of values is the first thing to report about any data set. It is also the number you divide by for the mean.
StatementTrue or false?
The mean is the fair share of all the values.?
To find the median, you must put the values in order first.?
The median of Raven's scores is 7.?
The mean of Rocket's second round, 3, 9, 9, 10, 9, is 9.?
The mean and the median are always the same number.?
WHY THIS EXERCISEKnowing when the mean and the median differ tells you something about the shape of the data.
Try it
Count out beans for Rocket's second round: piles of 3, 9, 9, 10 and 9.
Level the piles by moving beans. What height do you reach? Compare it with the middle pile when they are in order.

Two ways to name a middle. Tomorrow you measure how far the data spreads out around it.