Calculating variance and standard deviation for ungrouped and grouped data, using the given mean, and interpreting measures of central tendency and dispersion.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Two classes can have the same mean mark but very different results. Standard deviation measures how far the marks spread around that mean.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
σ² = Σ(x − x̄)²/n = Σx²/n − x̄².
σ = √σ².
σ² = Σfx²/Σf − x̄².
Use class midpoints; the result is an estimate.
x + k: mean + k, σ same. kx: mean × k, σ × k.
Larger σ = more spread / less consistent.
Mean (symmetric) or median (skewed).
σ, IQR, range.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (26 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [13 marks]
The table shows the marks x, out of 5, of 20 students: x = 1, 2, 3, 4, 5 with f = 2, 5, 8, 4, 1.
(a) Calculate the mean mark. [3]
(b) Calculate the variance and standard deviation, to 3 decimal places. [5]
(c) A second class has mean 2.85 and standard deviation 1.8. Compare the two classes. [3]
(d) Each mark is increased by 2. State the new mean and the new standard deviation. [2]
Question 2 [13 marks]
Answer all parts.
(a) The values 12, 15, 11, 18 and 14 have a mean of 14. Use the mean to calculate the variance and standard deviation. [5]
(b) Calculate the mean and standard deviation of the heights: 140–149 (6), 150–159 (10), 160–169 (14), 170–179 (7), 180–189 (3), using class midpoints. [6]
(c) Explain why the standard deviation for grouped data is only an estimate. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.