| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate variance from summary statistics |
| Difficulty | Easy -1.2 This is a straightforward S1 statistics question testing standard recall and application of basic formulas. Parts (i)-(iv) involve direct substitution into mean/variance formulas and linear transformations, while parts (v)-(vi) require routine cumulative frequency graph construction and reading. All techniques are standard textbook exercises with no problem-solving insight required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers2.02j Clean data: missing data, errors |
| Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
| 9.2 | 7.1 | 10.7 | 14.2 | 16.6 | 21.8 | 22.0 | 22.6 | 21.1 | 17.4 | 10.1 | 7.8 |
| Hours \(h\) | \(70 \leqslant h < 100\) | \(100 \leqslant h < 110\) | \(110 \leqslant h < 120\) | \(120 \leqslant h < 150\) | \(150 \leqslant h < 170\) | \(170 \leqslant h < 190\) |
| Number of years | 6 | 8 | 10 | 11 | 10 | 3 |
1 The maximum temperatures $x$ degrees Celsius recorded during each month of 2005 in Cambridge are given in the table below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Jan & Feb & Mar & Apr & May & Jun & Jul & Aug & Sep & Oct & Nov & Dec \\
\hline
9.2 & 7.1 & 10.7 & 14.2 & 16.6 & 21.8 & 22.0 & 22.6 & 21.1 & 17.4 & 10.1 & 7.8 \\
\hline
\end{tabular}
\end{center}
These data are summarised by $n = 12 , \Sigma x = 180.6 , \Sigma x ^ { 2 } = 3107.56$.\\
(i) Calculate the mean and standard deviation of the data.\\
(ii) Determine whether there are any outliers.\\
(iii) The formula $y = 1.8 x + 32$ is used to convert degrees Celsius to degrees Fahrenheit. Find the mean and standard deviation of the 2005 maximum temperatures in degrees Fahrenheit.\\
(iv) In New York, the monthly maximum temperatures are recorded in degrees Fahrenheit. In 2005 the mean was 63.7 and the standard deviation was 16.0 . Briefly compare the maximum monthly temperatures in Cambridge and New York in 2005.
The total numbers of hours of sunshine recorded in Cambridge during the month of January for each of the last 48 years are summarised below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Hours $h$ & $70 \leqslant h < 100$ & $100 \leqslant h < 110$ & $110 \leqslant h < 120$ & $120 \leqslant h < 150$ & $150 \leqslant h < 170$ & $170 \leqslant h < 190$ \\
\hline
Number of years & 6 & 8 & 10 & 11 & 10 & 3 \\
\hline
\end{tabular}
\end{center}
(v) Draw a cumulative frequency graph for these data.\\
(vi) Use your graph to estimate the 90th percentile.
\hfill \mbox{\textit{OCR MEI S1 Q1 [18]}}