← Back to course
Statistics 9-12 / Week 01 / Monday
1/6
Week 01 · Shape, Center and Spread

Monday

Three pictures of one data set
// Lap times in Nova's log
⏱ about 20 min

Monday: Three Pictures of One Data Set

Mist hangs over the park loop at seven. Comet stands at the gate cone with a stopwatch.

"Eleven practice laps on the short loop," she says. "One click each time I pass the cone. Nova, log them."

Nova hovers, a glowing tally on her side. "Logged. In order: 52, 54, 55, 55, 56, 56, 56, 57, 57, 58, 60 seconds."

Wren stacks a dot for each lap on a clipboard. "What do you notice?"

"They bunch at 56," Comet says. "A few spread out on each side. It looks like a small hill."

"One data set, three pictures," Wren says. "Dots, bars and a box. Each one shows something the others hide."

Nova dims her glow. "Would you like a hint? Start by putting every lap time in order."

"What can we make?" Comet asks. "A plot of every practice lap before the fun run."

Comet clicks a stopwatch as a runner passes a cone while Wren draws a dot plot and Nova shows a tally.

The crew's Tuesday lap times

Every number this week is the crew's own made-up reading from Nova's Run Log. These are Comet's eleven laps on the short loop, in seconds, already in order.

Lap1234567891011
Seconds5254555556565657575860
A dot plot of Comet's laps from 52 to 60 seconds, with the tallest stack at 56.

A solved problem to study

Here is how Wren turns the same eleven values into a box plot. Study each step before you try your own.

  1. Put the values in order. The least is 52 and the greatest is 60.
  2. Find the median, the middle value. With 11 values, it is the 6th: 56.
  3. Find the first quartile, the median of the lower five values: 55.
  4. Find the third quartile, the median of the upper five values: 57.
  5. Draw a box from 55 to 57 with a line at 56. Draw whiskers out to 52 and 60.
A box plot of Comet's laps: least 52, quartiles 55 and 57, median 56, greatest 60.

The histogram sorts the values into bins of equal width and draws a bar for each count. Here the bins are 3 seconds wide.

Bin 50 to 52 holds 1 lap. Bin 53 to 55 holds 3. Bin 56 to 58 holds 6. Bin 59 to 61 holds 1.

The dot plot keeps every value. The histogram trades detail for a clear shape. The box plot shows the middle half at a glance.

A histogram of Comet's laps in 3-second bins, with the tallest bar over 56 to 58.
READ THE PLOTS
  • Read the question.
  • Tap your answer.
Comet's laps are 52, 54, 55, 55, 56, 56, 56, 57, 57, 58, 60 seconds. What is the median?
Comet's laps are 52, 54, 55, 55, 56, 56, 56, 57, 57, 58, 60 seconds. What is the range, greatest minus least?
Comet's laps are 52, 54, 55, 55, 56, 56, 56, 57, 57, 58, 60 seconds. What is the first quartile?
Comet's laps are 52, 54, 55, 55, 56, 56, 56, 57, 57, 58, 60 seconds. What is the third quartile?
WHICH PLOT SHOWS IT?
  • Read the question.
  • Tap your answer.
Which plot keeps every single value visible?
Which plot shows the five-number summary and nothing else?
Which plot groups the values into equal-width bins?
How many of Comet's laps took exactly 56 seconds? Type the number.
WHY THIS EXERCISEThe dot plot answers "how many at this value" instantly. The box plot cannot.
StatementTrue or false?
A box plot shows the least value, the quartiles, the median and the greatest value.?
57 - 55 = 2?
A histogram shows each value as its own dot.?
In a dot plot, a taller stack means more values at that number.?
WHY THIS EXERCISEKnowing what each plot hides is as useful as knowing what it shows.
Try it
On graph paper, draw a number line from 50 to 62. Stack a dot for each of Comet's laps.
Under it, draw the box plot with the box from 55 to 57. Check that the two pictures agree.

A strong start. Tomorrow you measure the center and the spread with numbers, two different ways.