CAIE S1 2014 November — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionNovember
TopicMeasures of Location and Spread
TypeCumulative frequency graph construction then interpretation

6 On a certain day in spring, the heights of 200 daffodils are measured, correct to the nearest centimetre. The frequency distribution is given below.
Height \(( \mathrm { cm } )\)\(4 - 10\)\(11 - 15\)\(16 - 20\)\(21 - 25\)\(26 - 30\)
Frequency2232784028
  1. Draw a cumulative frequency graph to illustrate the data.
  2. \(28 \%\) of these daffodils are of height \(h \mathrm {~cm}\) or more. Estimate \(h\).
  3. You are given that the estimate of the mean height of these daffodils, calculated from the table, is 18.39 cm . Calculate an estimate of the standard deviation of the heights of these daffodils.