Construct stem-and-leaf then find median and quartiles

2 The numbers of people travelling on a certain bus at different times of the day are as follows.

1. Draw a stem-and-leaf diagram to illustrate the information given above.
2. Find the median, the lower quartile, the upper quartile and the interquartile range.
3. State, in this case, which of the median and mode is preferable as a measure of central tendency, and why.

5 The following are the annual amounts of money spent on clothes, to the nearest \(
) 10$, by 27 people.

1. Construct a stem-and-leaf diagram for the data.
2. Find the median and the interquartile range of the data. An 'outlier' is defined as any data value which is more than 1.5 times the interquartile range above the upper quartile, or more than 1.5 times the interquartile range below the lower quartile.
3. List the outliers.

2 In a survey 55 students were asked to record, to the nearest kilometre, the total number of kilometres they travelled to school in a particular week. The results are shown below.

1. On the grid, draw a box-and-whisker plot to illustrate the data.
   \includegraphics[max width=\textwidth, alt={}, center]{246c92f4-7603-43ff-8533-042a4be99a69-04_512_1596_900_262} An 'outlier' is defined as any data value which is more than 1.5 times the interquartile range above the upper quartile, or more than 1.5 times the interquartile range below the lower quartile.
2. Show that there are no outliers.

5 The pulse rates, in beats per minute, of a random sample of 15 small animals are shown in the following table.

1. Draw a stem-and-leaf diagram to represent the data.
2. Find the median and the quartiles.
3. On graph paper, using a scale of 2 cm to represent 10 beats per minute, draw a box-and-whisker plot of the data.

5 The number of Olympic medals won in the 2012 Olympic Games by the top 27 countries is shown below.

1. Draw a stem-and-leaf diagram to illustrate the data.
2. Find the median and quartiles and draw a box-and-whisker plot on the grid.
   \includegraphics[max width=\textwidth, alt={}, center]{4c2afa86-960c-473e-970c-ed16c8434fec-07_1006_1406_1007_411}

4 Prices in dollars of 11 caravans in a showroom are as follows.
\(\begin{array} { l l l l l l l l l l l } 16800 & 18500 & 17700 & 14300 & 15500 & 15300 & 16100 & 16800 & 17300 & 15400 & 16400 \end{array}\)

1. Represent these prices by a stem-and-leaf diagram.
2. Write down the lower quartile of the prices of the caravans in the showroom.
3. 3 different caravans in the showroom are chosen at random and their prices are noted. Find the probability that 2 of these prices are more than the median and 1 is less than the lower quartile.

2 The mean daily maximum temperatures at a research station over a 12 -month period, measured to the nearest degree Celsius, are given below.

1. Construct a sorted stem and leaf diagram to represent these data, taking stem values of \(0,10 , \ldots\).
2. Write down the median of these data.
3. The mean of these data is 24.3. Would the mean or the median be a better measure of central tendency of the data? Briefly explain your answer.

1 A camera records the speeds in miles per hour of 15 vehicles on a motorway. The speeds are given below. $$\begin{array} { l l l l l l l l l l l l l l l } 73 & 67 & 75 & 64 & 52 & 63 & 75 & 81 & 77 & 72 & 68 & 74 & 79 & 72 & 71 \end{array}$$

1. Construct a sorted stem and leaf diagram to represent these data, taking stem values of \(50,60 , \ldots\).
2. Write down the median and midrange of the data.
3. Which of the median and midrange would you recommend to measure the central tendency of the data? Briefly explain your answer.

1 The mean daily maximum temperatures at a research station over a 12-month period, measured to the nearest degree Celsius, are given below.

1. Construct a sorted stem and leaf diagram to represent these data, taking stem values of \(0,10 , \ldots\).
2. Write down the median of these data.
3. The mean of these data is 24.3 . Would the mean or the median be a better measure of central tendency of the data? Briefly explain your answer.

5 At a tourist information office the numbers of people seeking information each hour over the course of a 12-hour day are shown below. $$\begin{array} { l l l l l l l l l l l l } 6 & 25 & 38 & 39 & 31 & 18 & 35 & 31 & 33 & 15 & 21 & 28 \end{array}$$

1. Construct a sorted stem and leaf diagram to represent these data.
2. State the type of skewness suggested by your stem and leaf diagram.
3. For these data find the median, the mean and the mode. Comment on the usefulness of the mode in this case.

1 The lengths, in centimetres, of 18 snakes are given below. $$\begin{array} { l l l l l l l l l l l l l l l l l l } 24 & 62 & 20 & 65 & 27 & 67 & 69 & 32 & 40 & 53 & 55 & 47 & 33 & 45 & 55 & 56 & 49 & 58 \end{array}$$

1. Draw an ordered stem-and-leaf diagram for the data.
2. Find the mean and median of the lengths of the snakes.
3. It was found that one of the lengths had been measured incorrectly. After this length was corrected, the median increased by 1 cm . Give two possibilities for the incorrect length and give a corrected value in each case.