Question 1 - A-Level Maths

Exam Board	Edexcel
Module	S1 (Statistics 1)
Year	2023
Session	January
Topic	Data representation
Type	Complete frequency table from histogram only

The histogram shows the times taken, \(t\) minutes, by each of 100 people to swim 500 metres.
\includegraphics[max width=\textwidth, alt={}, center]{c316fa29-dedc-4890-bd82-31eb0bb819f9-02_986_1070_342_424}
1. Use the histogram to complete the frequency table for the times taken by the 100 people to swim 500 metres.
Time taken ( \(\boldsymbol { t }\) minutes) \(5 - 10\) \(10 - 14\) \(14 - 18\) \(18 - 25\) \(25 - 40\)
Frequency ( \(\boldsymbol { f }\) ) 10 16 24
Estimate the number of people who took less than 16 minutes to swim 500 metres.
Find an estimate for the mean time taken to swim 500 metres. Given that \(\sum f t ^ { 2 } = 41033\)
find an estimate for the standard deviation of the times taken to swim 500 metres. Given that \(Q _ { 3 } = 23\)
use linear interpolation to estimate the interquartile range of the times taken to swim 500 metres.

Time taken ( \(\boldsymbol { t }\) minutes)	\(5 - 10\)	\(10 - 14\)	\(14 - 18\)	\(18 - 25\)	\(25 - 40\)
Frequency ( \(\boldsymbol { f }\) )	10	16	24