Grade 9: Statistics

Warm up with a few quick statistics warm-ups on the board while the class settles, so every child starts thinking about the skill.

A boxplot summarises a data set using five key values (minimum, lower quartile, median, upper quartile, maximum), letting you compare the centre and spread of two or more data sets at a glance rather than listing every point. Model the method clearly, thinking aloud:

• Review finding a median on sorted data first, since a quartile is just a median of a half.
• Teach the five-number summary in order: minimum, Q1 (median of the lower half), median, Q3 (median of the upper half), maximum.
• Introduce the interquartile range (IQR = Q3 - Q1) as a spread measure that resists outliers better than the full range.
• Compare two data sets with the same median but different IQRs, so students see that 'centre' and 'spread' are separate ideas.
• Only once the numbers are secure, connect them to the visual boxplot (a box from Q1 to Q3 with whiskers to the min and max).

Work this through step by step on the board, then have the class talk you through a second one.

• Sorted data: 12, 15, 18, 22, 25, 29, 33, 38
• Minimum = 12, maximum = 38
• Median = (22 + 25) / 2 = 23.5
• Q1 = median of 12, 15, 18, 22 = (15 + 18) / 2 = 16.5
• Q3 = median of 25, 29, 33, 38 = (29 + 33) / 2 = 31
• IQR = 31 - 16.5 = 14.5

Do the first few questions of the practice worksheet together, one child explaining each step. Check for understanding before releasing the class to work alone.

Students complete the practice worksheet independently while you circulate and support.

Circulate and look for these, they are the usual sticking points:

• Forgetting to sort the data before finding any of the five numbers.
• Adding the two squares instead of subtracting when finding the IQR (Q3 - Q1, not Q3 + Q1).
• Assuming a bigger range always means a bigger IQR, missing that one outlier can inflate the range while barely changing the IQR.
• Comparing only the medians of two data sets and ignoring the spread (IQR) entirely.

Pull the class back together. Ask one child to explain statistics in their own words, pose a single check question everyone answers on a mini whiteboard, and name what you will build on next lesson.

Use the independent worksheet as the evidence. A child who can complete it accurately and explain one answer has met the objective; anyone who cannot needs the easier level and a short reteach next session.