SPS SPS SM Statistics 2025 April — Question 2 5 marks

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2025
SessionApril
Marks5
TopicData representation
TypeTotal sample size from histogram
DifficultyEasy -1.2 This is a straightforward histogram interpretation question requiring students to use frequency density to find frequencies. Part (a) involves a simple calculation using the relationship frequency = frequency density × class width. Part (b) requires slightly more work by splitting the calculation across two class intervals, but both parts are standard textbook exercises with no conceptual challenges beyond basic histogram mechanics.
Spec2.02b Histogram: area represents frequency

The histogram shows information about the lengths, \(l\) centimetres, of a sample of worms of a certain species. \includegraphics{figure_2} The number of worms in the sample with lengths in the class \(3 \leq l < 4\) is 30.
  1. Find the number of worms in the sample with lengths in the class \(0 \leq l < 2\). [2]
  2. Find an estimate of the number of worms in the sample with lengths in the range \(4.5 \leq l < 5.5\). [3]

The histogram shows information about the lengths, $l$ centimetres, of a sample of worms of a certain species.

\includegraphics{figure_2}

The number of worms in the sample with lengths in the class $3 \leq l < 4$ is 30.

\begin{enumerate}[label=(\alph*)]
\item Find the number of worms in the sample with lengths in the class $0 \leq l < 2$. [2]

\item Find an estimate of the number of worms in the sample with lengths in the range $4.5 \leq l < 5.5$. [3]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM Statistics 2025 Q2 [5]}}