Unit 2
4 marks · Normal2. The heights (in metres) of five sunflowers are measured and shown below: 1.24, 1.09, 1.32, 1.14, 1.28. A sixth sunflower grows to metres.
Calculate the mean height of the five sunflowers.
If the mean increases to 1.25 metres after adding the sixth sunflower, find the value of .
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 1.214
(b) 1.46
Common mistakes: Dividing by wrong number of values for mean
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly adds all five heights.
A1 (a) · 1 mark · Divides by 5 for mean; answer 1.214 (to three decimal places).
M2 (b) · 1 mark · Correctly sets up the equation (sum of five heights + h)/6 = 1.25. (follow-through)
A2 (b) · 1 mark · Solves for h = 1.46. (follow-through)
Worked solution
a)
metres
b) Let be the sixth height. New mean:
. Rounding to match significant figures: 1.46 (or 1.43, based on textbook marking).