Skills / Ages 11 to 14 / Math
Mean and median
Two ways to give one number for the middle of a list. The mean is the fair share: add every value and divide by how many there are. The median is the middle value once the list is in order.
Why it matters
The workbook's last statistics lesson writes a full summary of a data set, and the summary is built on these two numbers. It also chooses between them, because one far-off value drags the mean but barely moves the median. Your child needs both working before that choice can make sense.
What it looks like when your child can do it
- Given pages read on five nights, your child adds them, counts five values, divides, and checks by multiplying back.
- Asked for a median, your child puts the list in order before looking for the middle, every time.
- With an even count, your child takes the two middle values and finds the number halfway between them.
How to teach it at the kitchen table
- 01
Show the mean as a fair share
Build towers of blocks or coins with 2, 4, 5, 7 and 7 in them. Move pieces between towers until all five are the same height. Each one ends up with 5. That even height is the mean.
- 02
Add, count, divide
On paper the mean is three moves. Add every value, count how many values there are, and divide the total by the count. For 2, 4, 5, 7 and 7, that is 25 ÷ 5 = 5.
- 03
Check by multiplying back
The mean times the count gives the total back: 5 x 5 = 25, which matches. If the check fails, look at the count first. Dividing by the wrong number is the usual slip.
- 04
Order first, then find the middle
The median is a position, so sort the list from smallest to largest first. With an odd count, cross off one value from each end until one is left. For 9, 3, 7, 5, 8, sorted to 3, 5, 7, 8, 9, the median is 7.
- 05
Handle an even count
With an even count, two values share the middle. The median is halfway between them: add the two and divide by 2. For 4, 6, 8, 12 the middle pair is 6 and 8, so the median is 7, a number not on the list, and that is fine.
You will need: Paper and a pencil · Blocks, coins or crackers for leveling towers · Index cards for sorting values
Try it together
Try 1
Your child read 13, 15, 9, 14 and 9 pages on five nights. Find the mean.
Listen for 12 pages. The total is 13 + 15 + 9 + 14 + 9 = 60, and 60 ÷ 5 = 12. Check: 12 x 5 = 60. Watch that your child divides by 5, the count of nights.
Try 2
Find the median of the same five nights.
Listen for 13 pages. In order the list is 9, 9, 13, 14, 15, and the middle value is 13. A child who says 9, the middle of the list as it was written, skipped the sort.
Try 3
Hours of sleep on four nights were 9, 8, 10 and 7. Find the median.
Listen for 8.5 hours. In order the list is 7, 8, 9, 10. The two middle values are 8 and 9, and halfway between them is (8 + 9) ÷ 2 = 8.5. A median that is not on the list is correct.
Try 4
Minutes of piano practice on five days were 20, 25, 30, 25 and 100. Find the mean and the median. Which one describes a typical day better?
Listen for The mean is 40 minutes, because the total is 200 and 200 ÷ 5 = 40. The median is 25 minutes, from the ordered list 20, 25, 25, 30, 100. The median fits a typical day better, because the one long day dragged the mean up.
Try 5
The mean of four nights of reading was 10 pages. Three of the nights were 8, 12 and 9 pages. How many pages were read on the fourth night?
Listen for 11 pages. The mean times the count gives the total: 10 x 4 = 40. The three known nights make 8 + 12 + 9 = 29, and 40 - 29 = 11. Check: 8 + 12 + 9 + 11 = 40, and 40 ÷ 4 = 10.
Watch for
- Taking the middle of the list as it was written. The median only means something once the list is sorted.
- Dividing by the wrong count, often after leaving a value out of the total. Counting the values first prevents both.
If it is not there yet
- Go back to leveling towers of blocks or coins, so the mean is something your child can see. Use totals that share out evenly until the idea settles.
- For the median, write each value on a card, have your child line the cards up in order, and remove one card from each end until the middle is left.
- If the dividing itself is what trips your child up, back up to division with whole numbers before returning to the mean.
A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.
Where this skill comes up
Grade 6 Math Practice Workbook · Lesson 33
Summarizing a Data Set, Start to Finish
Needs it because the summary is built on the measures of center.