9. Statistics

For shirt colours blue, red, blue, green, red, blue, the tallies give blue 3, red 2 and green 1. The frequency column contains $3,2,1$—not the tally symbols themselves. Their sum is 6, matching the six observations.

In a two-way table, each row total is the sum across its cells and each column total is the sum down its cells. The sum of all row totals and the sum of all column totals must both equal the grand total. Use subtraction from a known total to find a missing cell only after identifying the correct row or column.

The table shows February has the greatest rainfall, while March has the most rainy days. Therefore 'the month with most rainfall also has most rainy days' is false for these data. A useful inference cites the values or pattern that justify it.

Set A is less variable because its range is smaller: $12$ compared with $30$. A lower range means the observed values are packed into a narrower span, but it does not say that every A value is close to every other value.

When comparing graphs, also use like-for-like features such as the modal category, peaks, gaps or overall pattern. Two comments should describe genuinely different features rather than repeat the same comparison in new words.

For values $24,25,26,27,98$, the mean is $40$ but the median is $26$. The single value $98$ pulls the mean upward, so calling $40$ a typical value would misrepresent most observations.

For the ordered data $3,4,4,6,8$, the total is $25$. Therefore the mean is $25\div5=5$, the median is $4$, the mode is $4$, and the range is $8-3=5$. Always order a list before locating its median.

For this ungrouped frequency table, $\sum f=6$ and $\sum fx=21$, so the mean is $21\div6=3.5$. The ordered positions are $2,3,3,3,5,5$, so the median and mode are both $3$, and the range is $5-2=3$. Frequencies count repeated observations; do not average the headings alone.

For frequencies $9,14,7$, the total is $30$. The sector angles are $9\div30\times360^\circ=108^\circ$, $14\div30\times360^\circ=168^\circ$ and $7\div30\times360^\circ=84^\circ$. They sum to $360^\circ$, which checks the chart.

For $13,15,21,21,28,31$, use stems $1,2,3$ and ordered leaves: $1\mid3\ 5$, $2\mid1\ 1\ 8$, $3\mid1$. The key $1\mid3=13$ fixes the place value. Every original value must appear exactly once.

Read the whole cloud of points before describing it. State the variables and direction, for example: 'as time in the shop increases, the number of items bought tends to increase.' A point far from the overall pattern is an unusual point; identify it from its coordinates.

If higher temperature is generally paired with more ice creams sold, the correlation is positive. If greater car power is generally paired with a shorter acceleration time, it is negative. Judge the trend of the whole cloud, not the slope between two selected points.

To estimate $y$ from a given $x$, start at the $x$-axis value, move vertically to the line, then move horizontally to the $y$-axis and read the scale. Reverse these moves to estimate $x$ from $y$. An estimate is approximate, so report a precision justified by the scale.

If the best-fit line for two test scores crosses near $(40,48)$, a test 1 score of $40$ gives an estimated test 2 score of about $48$. The estimate comes from the line, not from choosing the nearest plotted student.