A student reads 40, 43, 45, 47 and 52 pages on five days. Find the standard deviation using the assumed mean method.

1. 1 · Write what is given and what is to be found n = 5 values: 40, 43, 45, 47, 52. To find: σ by the assumed mean method.
2. 2 · Write the formula σ = √(Σd²/n − (Σd/n)²), where d = x − A.
3. 3 · Make the table
   • Take A = 45, the middle value.
   • d = x − 45: −5, −2, 0, 2, 7, so Σd = 2
   • d²: 25, 4, 0, 4, 49, so Σd² = 82
4. 4 · Substitute
   • σ = √(82/5 − (2/5)²)
   • = √(16.4 − 0.16) = √16.24
5. 5 · Work out the root
   • σ ≈ 4.03 pages
6. 6 · Check and box the answer The mean is 45 + 2/5 = 45.4, and the values lie about 4 pages either side of it. σ ≈ 4.03 pages.

Scoring tip: Draw a neat table with columns x, d and d². Write Σd and Σd² at the foot of the columns; much of the credit is for this table.