7th grade · Math · Unit 12 of 20
Center & Spread
Mean, median, range and IQR
What your child practices
Telling a statistical question from a regular question, and describing data with the mean, median, range and interquartile range.
New York State Learning Standards learning standard: NY-7.SP.1; NY-7.SP.4 · finding the interquartile range, spotting outliers, and describing data with measures of center and variability
How we explain it
Children can open this short lesson before they practice.
- Mean: add the values and divide by how many there are.
- Median: the middle value in order. Range: greatest − least.
- IQR: Q3 − Q1, the spread of the middle half.
Example: What is the mean of 4, 7, 9 and 12? 4 + 7 + 9 + 12 = 32. 32 ÷ 4 = 8. Answer: 8
Center & Spread in New York
In the New York State Learning Standards, this is unit 12 of 20 in 7th grade Math, after Mean, Median & Mode and before Multiply & Divide Signed Numbers.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
What is the mean of 5, 10, 12, 8, 10?
- 9
- 12
- 11
- 7
- 10
9
Hint: Add them (45) and divide by 5.
Question 2
What is the interquartile range (IQR) of 33, 1, 13, 39, 19, 3, 31, 24?
- 8
- 38
- 21
- 24
- 32
24
Hint: Order the data. Q1 = 8 (middle of the lower half), Q3 = 32 (middle of the upper half). IQR = Q3 − Q1.
Question 3
Which is a statistical question?
- What time does school start?
- How many minutes does it take students at my school to get to school?
- How many days are in a leap year?
- How many students are in Room 12?
How many minutes does it take students at my school to get to school?
Hint: A statistical question expects answers that vary, so you collect data to answer it.
Question 4
The data 12, 12, 17, 19, 19, 80 has one very large value. Which measure describes the typical value best?
- The median
- The range
- The mean
The median
Hint: One extreme value pulls the mean and range a long way, but the median barely moves.
Question 5
What is the median of 8, 20, 27, 27, 21?
- 21
- 20
- 21.5
- 27
- 22
21
Hint: Put the numbers in order. The median is the middle one (or the mean of the two middle ones).
Question 6
What is the range of 53, 32, 25, 12, 55, 49?
- 55
- 40.5
- 46
- 43
- 44
43
Hint: Range = greatest − least.