Question 7 - A-Level Maths

OCR MEI S1 2012 January — Question 7 19 marks

Exam Board	OCR MEI
Module	S1 (Statistics 1)
Year	2012
Session	January
Marks	19
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Data representation
Type	Outliers from cumulative frequency diagram
Difficulty	Moderate -0.3 This is a standard cumulative frequency question requiring routine reading from diagrams, calculating median/quartiles, applying the 1.5×IQR outlier rule, and making basic comparisons. All techniques are textbook exercises with no novel problem-solving required, though the multi-part nature and conceptual understanding of outliers elevates it slightly above pure recall.
Spec	2.02a Interpret single variable data: tables and diagrams 2.02f Measures of average and spread 2.02h Recognize outliers 2.02i Select/critique data presentation

7 The birth weights of 200 lambs from crossbred sheep are illustrated by the cumulative frequency diagram below. \includegraphics[max width=\textwidth, alt={}, center]{4b259fe3-73ef-419f-85ad-1a3b1e6ea56e-4_917_1146_367_447}

Estimate the percentage of lambs with birth weight over 6 kg .
Estimate the median and interquartile range of the data.
Use your answers to part (ii) to show that there are very few, if any, outliers. Comment briefly on whether any outliers should be disregarded in analysing these data. The box and whisker plot shows the birth weights of 100 lambs from Welsh Mountain sheep. \includegraphics[max width=\textwidth, alt={}, center]{4b259fe3-73ef-419f-85ad-1a3b1e6ea56e-4_328_1616_1749_260}
Use appropriate measures to compare briefly the central tendencies and variations of the weights of the two types of lamb.
The weight of the largest Welsh Mountain lamb was originally recorded as 6.5 kg , but then corrected. If this error had not been corrected, how would this have affected your answers to part (iv)? Briefly explain your answer.
One lamb of each type is selected at random. Estimate the probability that the birth weight of both lambs is at least 3.9 kg .

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7 The birth weights of 200 lambs from crossbred sheep are illustrated by the cumulative frequency diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{4b259fe3-73ef-419f-85ad-1a3b1e6ea56e-4_917_1146_367_447}\\
(i) Estimate the percentage of lambs with birth weight over 6 kg .\\
(ii) Estimate the median and interquartile range of the data.\\
(iii) Use your answers to part (ii) to show that there are very few, if any, outliers. Comment briefly on whether any outliers should be disregarded in analysing these data.

The box and whisker plot shows the birth weights of 100 lambs from Welsh Mountain sheep.\\
\includegraphics[max width=\textwidth, alt={}, center]{4b259fe3-73ef-419f-85ad-1a3b1e6ea56e-4_328_1616_1749_260}\\
(iv) Use appropriate measures to compare briefly the central tendencies and variations of the weights of the two types of lamb.\\
(v) The weight of the largest Welsh Mountain lamb was originally recorded as 6.5 kg , but then corrected. If this error had not been corrected, how would this have affected your answers to part (iv)? Briefly explain your answer.\\
(vi) One lamb of each type is selected at random. Estimate the probability that the birth weight of both lambs is at least 3.9 kg .

\hfill \mbox{\textit{OCR MEI S1 2012 Q7 [19]}}

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Q1 7 Q2 7 Q3 8 Q4 6 Q5 8 Q6 17 Q7 19