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Statistics 9-12 / Week 01 / Friday
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Week 01 · Shape, Center and Spread

Friday

Shapes all around the loop
// Lap times in Nova's log
⏱ about 20 min

Friday: Shapes All Around the Loop

"The sign-up sheet has a column for laps run this week," Comet says. "Eleven runners filled it in."

Wren reads the column. "2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7. What do you notice?"

"Most ran 3 to 5 laps," Comet says. "A couple ran 6 or 7. The tail points to the right."

"So the mean, 4.5, sits above the median, 4," Wren says. "Report the median and IQR for this one."

Nova projects a histogram with bins two laps wide. "Would you like a hint? Counts can be plotted just like times."

"Lap times, step counts, laps per runner," Comet says. "Any number that lands on a number line gets a plot."

"And every plot gets a shape, a center and a spread," Wren says. "That is the whole week in one sentence."

Counts are data too

Lap times are measured. Laps per runner are counted. Both are values on a number line, so both get the same three plots.

The eleven sign-up counts are 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7. The median is 4 and the quartiles are 3 and 6.

A dot plot of laps run this week from 2 to 7, with the tallest stack at 4.
A histogram of laps run this week in bins two laps wide, with the tallest bar over 4 to 5.

Review: the week in one table

QuestionSymmetric setSkewed set
Which center?meanmedian
Which spread?standard deviationIQR
Mean and medianclose togethermean pulled toward the tail
Which plot shows shape fastest?histogram or dot plothistogram or dot plot
  • Dot plot: one dot per value. Histogram: bars over equal-width bins. Box plot: the five-number summary.
  • Mean: sum ÷ n. Median: the middle value in order.
  • Standard deviation: square root of the mean of the squared distances (the crew divides by n). IQR: Q3 - Q1.
  • Compare groups by center and spread together. Let shape pick the measures.
MIXED REVIEW
  • Read the question.
  • Tap your answer.
The laps per runner are 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7. What is the median?
The laps per runner have quartiles 3 and 6. What is the IQR?
The laps per runner are 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7. What is the mean? (Round to 1 place.)
The laps per runner have mean 4.5 and median 4. What shape does the distribution have?
WHICH CONCLUSION IS JUSTIFIED?
  • Read the question.
  • Tap your answer.
Comet's laps have IQR 2 and Wren's have IQR 6. Which conclusion is justified?
A set's mean is well above its median. Which conclusion is justified?
Two groups have the same mean. Which conclusion is justified?
How many of the eleven runners ran exactly 4 laps? Type the number.
WHY THIS EXERCISEThe dot plot turns a sign-up column into a picture you can count from.
StatementTrue or false?
Laps per runner can be shown on a dot plot because each count is a number on a line.?
6 - 3 = 3?
For a skewed set, the mean is the better center to report.?
A histogram with bins two laps wide puts 4 laps and 5 laps in the same bar.?
WHY THIS EXERCISEThe review ties the three plots to the two pairs of measures.
Try it
On graph paper, draw the box plot of the laps per runner from 2 to 7.
Mark the mean with a small arrow. Notice which side of the median it lands on.
Draw a histogram of a count from your home, such as books per shelf, with bins two wide.

A full week of plots. Tomorrow is Track Day: show your family a dot plot of your own data.

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