State the following data as categorical or numerical.

the average temperature of a city in each month

A score was added to the set of scores: \( 13, 18, 20, 20, 22 \) and \( 26 \). The new mean is equal to \( 19\). What score was added?

Estimate the mean of the data.

\( \begin{array}{|c|c|c|c|c|c|} \hline
Class & 150 \le x < 200 & 200 \le x < 250 & 250 \le x < 300 & 300 \le x < 350 & 350 \le x < 400 \\ \hline Frequency (f) & 18 & 21 & 24 & 29 & 27 \\ \hline \end{array} \)

Select the corresponding frequency table for the cumulative frequency graph shown.

Find the interquartile range of the data represented in the box-and-whisker plot.

\( \begin{array}{c|cccccc}
1 & 0 & 1 &&&& \\
2 & 1 & 2 & 6 &&& \\
3 & 2 & 4 & 7 & 7 && \\
4 & 3 &&&&& \\
\end{array} \)

The table shows Amy’s results for two tests.   Which test is the better result for Amy compared to her class?

\( \begin{array}{|c|c|c|c|} \hline
\text{test} & \text{Amy’s result} & \text{class mean} & \text{class standard deviation} \\ \hline
A & 82 & 75 & 7 \\ \hline
B & 86 & 77 & 10 \\ \hline
\end{array} \)

Find the population standard deviation of the following data set, correcting to two decimal places using technology.

\(\begin{array} {|c|c|c|c|c|} \hline
score &10 \le x < 20 &20 \le x < 30 &30 \le x < 40 &40 \le x < 50 \\ \hline frequency &34 &37 &44 &21 \\ \hline \end {array} \)

7 cards numbered 2, 3, 4, 5, 6, 7, and 8 are placed in a hat. Two are taken simultaneously. Find the probability that both are odd. Answer to two decimal places.

Given  \(P\left( A \right) = \dfrac{1}{2}\) and \(P\left( B \right) = \dfrac{1}{3}\),   find  \(P\left( {A\text{ or }B} \right)\),   correcting to one decimal place.

Factory Ace produces tyres with a probability of 0.05 that a randomly selected tyre is faulty, while Factory Bro is 0.03. A retailer Charles buys 70 types from Ace and 30 from Bro. A customer purchases one of these tyres from Charles. Find the probability that this tyre is not faulty.