1. Categorical
2. Discrete numerical
3. Continuous numerical
4. Categorical
5. Continuous numerical
6. Discrete numerical (values come in fixed jumps)
7. A: $5$, B: $3$, C: $2$. Total $10$.
8. $15$
9. Column graph
10. Dot plot
11. $23,\ 25,\ 28$
12. Four data values of $7$ appeared in the sample.
13. $40$
14. It stretches small differences so bars look very different when they are actually close.

1. Size $6$: $1$, Size $7$: $4$, Size $8$: $5$, Size $9$: $4$, Size $10$: $1$.
2. $8$ (appears most often).
3. Roughly symmetrical around $8$.
4. $5$ dots.
5. A line graph would be inappropriate: shoe sizes are discrete, not a continuous change over time.

Questions 6-9 from the stem-and-leaf plot:

6. $15$ students.
7. Lowest $42$; highest $75$.
8. $53$ (two students scored $53$) and $61$ (two students scored $61$) - both are modes; the data is bimodal.
9. Range $= 75 - 42 = 33$.

1. A line graph would be better. Temperature varies continuously with time, so joining the hourly readings with a line shows the trend clearly. Columns with gaps suggest separate, independent categories rather than a single continuous variable.
2. Starting the $y$-axis at $49$ exaggerates tiny differences - the $50$-vs-$52$ gap becomes several times taller than it should. A reader glancing at the bar heights might think product $C$ sells vastly more than $A$, when it’s only $\tfrac{52 - 50}{50} = 4\%$ more. Always check whether the $y$-axis starts at zero before comparing bar heights.
3. Usually not. The mode is the most frequent value while an outlier is a value unusually far from the rest. In an extreme case (e.g. a dataset where one far value appears many times) a single value could be both - but in typical distributions the mode sits in the middle of the bulk, not at the tail.
4. Not in the arithmetic sense - you cannot average “red”, “blue”, “green”. You can count frequencies for each category and quote the mode (the most common category), but the mean and median don’t apply to purely categorical data.

1. $27$ students. Column graph: bars for each sport with heights $9, 7, 5, 4, 2$; $y$-axis shows frequency, $x$-axis shows sport.

2. Line graph (daily values over the week, with days on the $x$-axis). Total customers served: $42 + 38 + 45 + 50 + 65 + 80 + 60 = 380$.

3. Line graph. Maximum at $2$ p.m. ($27$ degC).

4. Stem-and-leaf plot:

   Stem | Leaf
     14 | 5 8 9
     15 | 0 0 0 2 3 5 5 6 8
     16 | 0 2

5. Line graph. It shows the trend (steady growth) over time clearly.