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 1Discrete Values
x = 0, 1, 2, 3, …
use the values directly
Type 2Grouped Data
e.g. 10 ≤ x < 20
use the midpoint of each interval
Type 3Raw 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
EASYA 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
MEDIUMThe 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
HARDA 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 ▲
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 ▲
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 ▲
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 ▲
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.
📖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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