1.

 a b c d e (i) 12 17.20 6.6 62 824 000 mg (ii) 5 12.48 4.2 48 9200 cg (iii) 20 20.60 9.6 86 986 g (iv) 15 8.12 5.4 38 894 g (v) 41 17.45 6.2 54 1409 g (vi) 14.01 15.8 6.63 65.5 697 g (vii) 11.3 5.78 2.26 18.6 472 g

2. 10th percentile is 10, 90th percentile is 58.

.3. Find the mean of 12, 14, 17, 20, 21, 24 and complete the table below to help to find the standard deviation.

 x x − (x − )2 12 12 − 18 = -6 36 14 14 − 18 = -4 16 17 17 − 18 = -1 1 20 20 − 18 = 2 4 21 21 − 18 = 3 9 24 24 − 18 = 6 36 Total      Σ(x − )2 = 102

Standard deviation s = 4.12 (to 3 sig.fig.)

4. Find the mean and standard deviation of the following frequency distribution. Complete the table to assist your calculation.

 x f x − (x − )2 f(x − )2 1 4 1 − 2.72 = -1.72 2.9584 11.8336 2 6 2 − 2.72 = -0.72 0.5184 3.1104 3 9 3 − 2.72 = 0.28 0.0784 0.7056 4 5 4 − 2.72 = 1.28 1.6384 8.192 5 1 5 − 2.72 = 2.28 5.1984 5.1984 Σ 25 29.04

Standard deviation s = 1.08 (to 3 sig.fig.)

5. Standard deviation s = 5.03 (to 3 sig. fig.)

6. Standard deviation s = 1.19 (to 3 sig. fig.)