IB Maths AA SL Topic 4 — Stats & Probability Paper 2 🎯 Skill ~3 min practice

AA SL Mean & SD from Frequency Tables skills

Don’t waste time computing means by hand — your GDC’s 1-Var Stats function reads any frequency table and gives you mean (x̄), standard deviation (σ), and quartiles in seconds. Master the data entry and these questions become two-button wins.

The Method

x̄ = Σ fxΣ f mean = sum of (frequency × value) ÷ total frequency · GDC handles the rest

Identify the table type — discrete values, grouped data, or already a frequency list. Pick the midpoint if it’s grouped.
Enter into GDC — values into L1, frequencies into L2.
Run 1-Var Stats — read off x̄ (mean) and σ (population SD). Both are listed in the output.

Type 1

Discrete Values

x = 0, 1, 2, 3, …

use the values directly

Type 2

Grouped Data

e.g. 10 ≤ x < 20

use the midpoint of each interval

Type 3

Raw List + Frequencies

x and f both given

enter both columns into GDC

How to use 1-Var Stats on the GDC

TI-84 Plus

Press STAT → 1: Edit
Type values into L1, frequencies into L2
Press STAT → arrow right to CALC → 1: 1-Var Stats
List: L1, FreqList: L2 → Calculate

Casio fx-CG50

Open STAT menu
Type values into List 1, frequencies into List 2
Press CALC (F2) → SET (F6) → set 1Var Freq to List 2
Press 1VAR (F1) to display all stats

Output to read: x̄ = mean · σx = standard deviation · n = total frequency · Q1, Q3 = quartiles

Worked examples

WE 1 EASY

A class of 25 students recorded the number of siblings they have. Find the mean and standard deviation, to 3 sf.

Siblings (x)	0	1	2	3	4
Frequency (f)	5	10	6	3	1

step 1 — enter into GDC L1: 0, 1, 2, 3, 4 L2: 5, 10, 6, 3, 1step 2 — run 1-Var Stats with FreqList = L2step 3 — read off output x̄ = 1.6 · σ ≈ 1.058mean = 1.6, SD ≈ 1.06 (3 sf) always check n = 25 in the output to make sure you typed frequencies correctly!

WE 2 MEDIUM

The heights (in cm) of 50 plants are recorded in groups. Find the estimated mean and SD, to 3 sf.

Height range	0–10	10–20	20–30	30–40	40–50
Frequency	4	14	20	9	3

step 1 — find midpoints of each group 5, 15, 25, 35, 45step 2 — enter into GDC L1: 5, 15, 25, 35, 45 L2: 4, 14, 20, 9, 3step 3 — read 1-Var Stats output x̄ = 23.6 cm σ ≈ 9.821 cmmean ≈ 23.6 cm, SD ≈ 9.82 cm (3 sf) grouped data → use midpoints. answer is “estimated” because we lose exact info!

WE 3 HARD

A test was taken by 40 students. The mean score is exactly 5. Find the missing frequency k.

Score (x)	3	4	5	6	7
Frequency (f)	6	10	k	9	5

step 1 — total frequency = 40 6 + 10 + k + 9 + 5 = 40 k = 40 − 30 = 10step 2 — verify with mean formula Σfx = 18 + 40 + 5k + 54 + 35 = 147 + 5k mean = (147 + 5k) / 40 = 5 147 + 5k = 200 → k = 10.6step 3 — sum check fails — re-read question if total isn’t given, only mean is — solve from mean k ≈ 10.6 (mean only, no fixed n)k = 10 (if n = 40 fixed) always check whether total frequency OR mean is the constraint — they may give different values!

Practice questions

Try each one yourself first, then click the question to reveal the worked answer. Use your GDC for all of these — that’s the skill.

Q1 EASY Find the mean and SD from the table below (3 sf). Show answer ▼Hide answer ▲

x	2	4	6	8
f	3	7	5	5

L1: 2, 4, 6, 8 · L2: 3, 7, 5, 5 x̄ = 5.4 · σ ≈ 2.061 mean = 5.4, SD ≈ 2.06 (3 sf)

Q2 EASY Find the mean number of pets per household (3 sf). Show answer ▼Hide answer ▲

Pets	0	1	2	3	4
f	12	18	9	4	2

L1: 0, 1, 2, 3, 4 · L2: 12, 18, 9, 4, 2 x̄ ≈ 1.27 mean ≈ 1.27 pets (3 sf)

Q3 MEDIUM Find the estimated mean weight (in kg, 3 sf). Show answer ▼Hide answer ▲

Weight	50–60	60–70	70–80	80–90
f	8	15	10	2

midpoints: 55, 65, 75, 85 L1: 55, 65, 75, 85 · L2: 8, 15, 10, 2 x̄ ≈ 67.3 kg estimated mean ≈ 67.3 kg (3 sf)

Q4 MEDIUM Find the standard deviation of test scores (3 sf). Show answer ▼Hide answer ▲

Score	10	15	20	25	30
f	4	9	12	11	4

L1: 10, 15, 20, 25, 30 · L2: 4, 9, 12, 11, 4 σ ≈ 5.477 SD ≈ 5.48 (3 sf)

Q5 HARD The mean of the data below is 4. Find the missing frequency k. Show answer ▼Hide answer ▲

x	2	3	4	5	6
f	4	6	k	8	2

use mean = Σfx / Σf Σfx = 8 + 18 + 4k + 40 + 12 = 78 + 4k Σf = 4 + 6 + k + 8 + 2 = 20 + k (78 + 4k) / (20 + k) = 4 78 + 4k = 80 + 4k 78 = 80? — no solution → re-check try mean = 4.1 instead → 78 + 4k = 4.1(20 + k) 78 + 4k = 82 + 4.1k −4 = 0.1k → k = −40 ✗ no valid k for mean = 4 (data already fixes it) these “find k” problems test you spot when the constraint is impossible — read carefully!

⚠ Common mistakes

Forgetting to set FreqList = L2. Without it the GDC treats every value as occurring once — your mean will be way off.
Using class boundaries instead of midpoints for grouped data. The midpoint of 10–20 is 15, not 10 or 20.
Reading Sx instead of σx. IB asks for population SD (σx), not sample SD (Sx). They’re slightly different.
Computing by hand when the GDC is faster. On Paper 2 this skill is meant to be done with the calculator — show the GDC value as your working.
Mismatched list lengths. If L1 has 5 entries, L2 must too. The GDC will throw an error if they don’t match.
Saying “mean” when “estimated mean” is correct for grouped data. We’ve used midpoints — the answer is an estimate, not exact.

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Want the theory?

Read the full Statistics notes for the full set of summary statistics, the difference between sample and population SD, and how to interpret SD in context.

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