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Data and Society 9-12 / Week 09 / Wednesday
3/6
Week 09 · Finding the Middle and the Pattern

Wednesday

Count Lab: Report a typical value
// Typical values, extreme values and what a pattern can prove
⏱ about 20 min

Wednesday: Count Lab: Report a Typical Value

The council asks for a second number: how often does a typical morning member visit?

Wren copies the Q4 answers from all 8 members who usually come in the morning onto a fresh sheet.

Comet cuts a sheet of scrap paper into eight slips. "One slip for each answer. Then we can slide them into order."

"What do you notice before we start?" Wren asks. "Is there an extreme value in this group too?"

Comet scans the column. "One member visited 21 times. Most of the others visited 7 times or fewer."

Nova hovers over the slips. "Would you like a hint?" she asks. "Find all three values first. Then decide which one tells the truest story."

Your mission

You will find the mean, median and mode for the morning group.

Then you will choose which one to report to the council and justify it in a sentence.

  • Paper and a pencil
  • Eight small paper slips (tear one sheet of scrap paper into eight pieces)
  • The morning table below
Morning memberQ4: Visits last week
M072
M157
M1614
M217
M220
M252
M3021
M343

Made-up data from the Commons Count story. The members are known only by ID.

PREDICT FIRST
  • Read the question.
  • Tap your answer.
Will the mean be bigger or smaller than the median for this group?
  1. Write each Q4 value on its own slip. Do not write any names, only the value.
  2. Slide the slips into order from smallest to largest.
  3. Add all eight values and write the sum.
  4. Divide the sum by 8 to find the mean.
  5. Find the 4th and 5th slips. The median is halfway between them.
  6. Count which value appears most often. That is the mode, and there may be more than one.
  7. Write all three values in a small table.
  8. Choose one to report and write one sentence that justifies it.
CHECK YOUR RESULTS
  • Read the question.
  • Tap your answer.
What is the sum of the eight values?
What is the mean?
What is the median?
What is the mode?
Lab checkTrue or false?
The 21 pulls the mean above the median.?
Six of the eight morning members visited 7 times or fewer.?
The median is the same as the mean for this group.?
To report a typical value fairly, the crew should drop M30's answer.?
WHY THIS EXERCISEChecking the result against the data is how you know your report is fair.
Sample reports
Report the median: "The typical morning member visited 5 times last week. One member visited 21 times, which pulls the mean up to 7."
Report all three: "Mean 7, median 5, modes 2 and 7. Half the morning members visited 3 times or fewer."
Either can be fair. A fair report says which value it uses and mentions the extreme value.
On paper, draw a number line from 0 to 22. Put a dot for each morning value, then mark the mean, the median and the modes.

Excellent lab work, data analyst. Tomorrow you will test what a pattern between two variables can prove.

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