Moderate -0.8 This is a straightforward cumulative frequency interpretation question requiring students to read median and quartiles from graphs, then calculate IQR and make simple comparisons. It involves standard statistical measures with no complex calculations or novel problem-solving—easier than average A-level content.
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The birth weights of random samples of 900 babies born in country \(A\) and 900 babies born in country \(B\) are illustrated in the cumulative frequency graphs. Use suitable data from these graphs to compare the central tendency and spread of the birth weights of the two sets of babies. [6]
median \(A = 2.0 - 2.1\) or \(\bar{x}_A = 2.0 - 2.1\)
Answer
Marks
Guidance
median \(B = 3.8 - 3.9\) or \(\bar{x}_B = 3.4 - 3.5\)
M1, A1
For finding medians or using mid-pts and freqs to find means, or seen 2 box-plots. Correct medians or means for \(A\) and \(B\)
Country \(B\) has heavier babies on average
B1
Correct statement allow '...higher median...' etc.
IQ range \(A = 2.4 - 1.5 = 0.9\) or sd \(= 0.5 - 0.7\)
Answer
Marks
Guidance
IQ range \(B = 4.5 - 2.2 = 2.3\) or sd \(= 1.2 - 1.4\)
M1, A1
Finding spreads by IQ range or range or sd or 2 box-plots. Correct IQ range or sd for \(A\) and \(B\) (\(\pm 0.1\) kg) or correct IQR on box-plots
Country \(B\) has greater spread of weights
A1 [6]
Correct statement
median $A = 2.0 - 2.1$ or $\bar{x}_A = 2.0 - 2.1$
median $B = 3.8 - 3.9$ or $\bar{x}_B = 3.4 - 3.5$ | M1, A1 | For finding medians or using mid-pts and freqs to find means, or seen 2 box-plots. Correct medians or means for $A$ and $B$
Country $B$ has heavier babies on average | B1 | Correct statement allow '...higher median...' etc.
IQ range $A = 2.4 - 1.5 = 0.9$ or sd $= 0.5 - 0.7$
IQ range $B = 4.5 - 2.2 = 2.3$ or sd $= 1.2 - 1.4$ | M1, A1 | Finding spreads by IQ range or range or sd or 2 box-plots. Correct IQ range or sd for $A$ and $B$ ($\pm 0.1$ kg) or correct IQR on box-plots
Country $B$ has greater spread of weights | A1 [6] | Correct statement
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\includegraphics{figure_3}
The birth weights of random samples of 900 babies born in country $A$ and 900 babies born in country $B$ are illustrated in the cumulative frequency graphs. Use suitable data from these graphs to compare the central tendency and spread of the birth weights of the two sets of babies. [6]
\hfill \mbox{\textit{CAIE S1 2010 Q3 [6]}}