# Exam-Style Question on Averages

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 266. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

The following table show data collected by a researcher about the length of monitor lizards living in a park in Bangkok.

Length (cm)Frequency
$$0\lt l \le 50$$9
$$50\lt l \le 100$$13
$$100\lt l \le 150$$22
$$150\lt l \le 200$$19
$$200\lt l \le 250$$11
$$250\lt l \le 300$$3

(a) Which is the modal group?

(b) Calculate an estimate for the mean lizard length.

(c) The researcher claims that the range of lengths must lie between 2m and 3m. Explain how the researcher came to this conclusion.

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