1 · Read the scale first
Before reading any bar, check what each grid line is worth. On this graph each line is 10, so a bar halfway between 30 and 40 shows 35.
Most graph mistakes come from counting grid lines as if each were 1.
2 · Mean (average)
Add the values and divide by how many there are. Scores 82, 90, 75, 93: the sum is 340, and 340 ÷ 4 = 85.
The mean is the level the bars would reach if you evened them out.
3 · Median, mode, and range
Median: put the numbers in order and take the middle one. For 7, 3, 9, 4, 8 → 3, 4, 7, 8, 9, the median is 7. With an even count, take halfway between the two middle numbers.
Mode: the value that appears most often. Range: greatest − least, here 9 − 3 = 6.
4 · A missing value from the mean
"The mean of 4 scores is 80. Three of them are 75, 82, and 88. What is the fourth?" The four must add to 4 × 80 = 320. The three add to 245, so the fourth is 75.
Mean × count = total. That one fact solves almost every "what score do you need" question.
5 · Probability as a fraction
Probability = (ways the thing can happen) ÷ (all the ways). A bag has 5 red, 3 blue, and 2 green marbles: P(blue) = 3/10.
It is not 1/3 just because there are three colors. Count the marbles, not the colors.
6 · "Not" and "or"
P(not blue) = 1 − P(blue). With 3 blue out of 10, the chance of not blue is 7/10.
P(red or green) adds the counts: 5 + 2 = 7, so 7/10.
7 · Probability words
A probability of 0 is impossible, 1 is certain, and 1/2 is an even chance. A spinner with 3 red sections out of 4 equal ones lands on red more likely than not.
8 · Counting combinations
4 shirts and 3 pairs of pants make 4 × 3 = 12 outfits: every shirt goes with every pair of pants.
Add a third choice, 2 hats, and multiply again: 12 × 2 = 24. Adding (4 + 3 + 2) counts the clothes, not the outfits.
9 · Handshakes and pairs
"5 friends each shake hands once with each other friend." Each person shakes 4 hands: 5 × 4 = 20, but that counts every handshake twice. The answer is 20 ÷ 2 = 10.
10 · What the data shows
A graph only supports statements about what was measured. If a survey asked 20 students in one class, it does not tell you about the whole school.
On the ISEE, the right choice is often the careful one: "more students chose soccer than tennis" rather than "most students love soccer".
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