Statistics: centre, spread and distributions

Which of these are statistical questions? (Choose all that apply.)

Six friends picked these numbers of mangoes: $4, 9, 6, 3, 8, 6$. What is the mean number of mangoes per friend?

Find the median of $12, 7, 3, 20, 9, 15$.

Using this lesson's rule for quartiles, find the interquartile range of $3, 5, 7, 8, 10, 12, 13, 15, 19$.

The data $3, 4, 5, 5, 6, 7, 8$ are minutes to walk to school. The $8$ is a typing error and should have been $80$. Which summaries change when it is corrected? (Choose all that apply.)

Two maize varieties are grown on 20 plots each. Variety P: median yield $3.1$ tonnes per hectare, IQR $0.4$. Variety Q: median $3.2$, IQR $1.8$. Which statement is the best comparison?

In a test, a class of $10$ students has a mean score of $60$ and a class of $30$ students has a mean score of $80$. What is the mean score of all $40$ students?

In the proof of Theorem 6 we expand $\sum (x_i - c)^2 = \sum (x_i - \bar x)^2 + 2(\bar x - c)\sum (x_i - \bar x) + n(\bar x - c)^2$. Why does the middle term vanish?

In Lean, median_resistant says: 3 ≤ l.length → medianSorted (l.set (l.length - 1) v) = medianSorted l. Why is the hypothesis 3 ≤ l.length needed?

Write five_number_summary(data) returning a tuple (minimum, Q1, median, Q3, maximum) using this lesson's rule: sort the data; the median is the middle value (or the mean of the two middle values); $Q_1$ and $Q_3$ are the medians of the lower and upper halves, leaving out the median when the number of values is odd. Use a helper median(values).