Draw box plot from raw data

4 The following are the house prices in thousands of dollars, arranged in ascending order, for 51 houses from a certain area.

1. Draw a box-and-whisker plot to represent the data. An expensive house is defined as a house which has a price that is more than 1.5 times the interquartile range above the upper quartile.
2. For the above data, give the prices of the expensive houses.
3. Give one disadvantage of using a box-and-whisker plot rather than a stem-and-leaf diagram to represent this set of data.

4 A random sample of 25 people recorded the number of glasses of water they drank in a particular week. The results are shown below.

1. Draw a stem-and-leaf diagram to represent the data.
2. On graph paper draw a box-and-whisker plot to represent the data.

6 The birth weights in kilograms of 25 female babies are shown below, in ascending order.

1. Find the median and interquartile range of these data.
2. Draw a box and whisker plot to illustrate the data.
3. Show that there is exactly one outlier. Discuss whether this outlier should be removed from the data. The cumulative frequency curve below illustrates the birth weights of 200 male babies. \includegraphics[max width=\textwidth, alt={}, center]{6b886da6-3fb8-4b4c-b572-f4b770ae5a4c-3_929_1569_1450_248}
4. Find the median and interquartile range of the birth weights of the male babies.
5. Compare the weights of the female and male babies.
6. Two of these male babies are chosen at random. Calculate an estimate of the probability that both of these babies weigh more than any of the female babies.

1. The stem and leaf diagram shows the ages of the 35 male passengers on a cruise.

Key: 1 | 3 represents an age of 13 years

1. Find the median age of the male passengers.
2. Show that the interquartile range (IQR) of these ages is 16 An outlier is defined as a value that is more than \(1.5 \times\) IQR above the upper quartile
   or \(1.5 \times\) IQR below the lower quartile
3. Show that there are 3 outliers amongst these ages.
4. On the grid in Figure 1 on page 9, draw a box plot for the ages of the male passengers on the cruise. Figure 1 on page 9 also shows a box plot for the ages of the female passengers on the cruise.
5. Comment on any difference in the distributions of ages of male and female passengers on the cruise.
   State the values of any statistics you have used to support your comment.
   (1) Anja, along with her 2 daughters and a granddaughter, now join the cruise.
   Anja's granddaughter is younger than both of Anja's daughters.
   Anja had her 23rd birthday on the day her eldest daughter was born.
   When their 4 ages are included with the other female passengers on the cruise, the box plot does not change.
6. State, giving reasons, what you can say about
   1. the granddaughter's age
   2. Anja's age.
      (3)
      \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{29ac0c0b-f963-40a1-beba-7146bbb2d021-09_1025_1593_1541_182} \captionsetup{labelformat=empty} \caption{Figure 1}
      \end{figure}

1 The number of passengers getting off the 11.45 am train at a railway station on each of 35 days is summarised as follows.

The following stem and leaf diagram shows the aptitude scores \(x\) obtained by all the applicants for a particular job.

1. Write down the modal aptitude score. [1]
2. Find the three quartiles for these data. [3]

Outliers can be defined to be outside the limits \(Q_1 - 1.0(Q_3 - Q_1)\) and \(Q_3 + 1.0(Q_3 - Q_1)\).

1. On a graph paper, draw a box plot to represent these data. [7]

For these data, \(\Sigma x = 3363\) and \(\Sigma x^2 = 238305\).

1. Calculate, to 2 decimal places, the mean and the standard deviation for these data. [3]
2. Use two different methods to show that these data are negatively skewed. [4]

In a survey of natural habitats, the numbers of trees in sixty equal areas of land were recorded, as follows:

1. Construct a stem-and-leaf diagram to illustrate this data, using the groupings 5 - 9, 10 - 14, 15 - 19, 20 - 24, etc. [8 marks]
2. Find the three quartiles for the distribution. [4 marks]
3. On graph paper construct a box plot for the data, showing your scale and clearly indicating any outliers. [4 marks]

The following data were collected by counting the number of cars that passed the gates of a college in 60 successive 5 minute intervals.

12	20	19	31	32	35	37	29	26	27	20	17
15	9	8	11	13	17	17	21	25	27	28	25
30	32	37	40	45	45	44	47	42	41	36	38
35	34	30	30	27	26	29	24	23	21	21	18
16	16	19	22	26	28	23	17	15	10	12	13

1. Make a stem and leaf diagram for this data, using the groups \(5-9\), \(10-14\), \(\ldots\), \(45-49\). Show the total in each group and give a key to the diagram. [7 marks]
2. Find the three quartiles for this data. [4 marks]
3. On graph paper, draw a box plot for the data. [4 marks]
4. Describe the skewness of the distribution. [1 mark]

Jane and Tahira play together in a basketball team. The list below shows the number of points that Jane scored in each of 30 games.

1. Construct a stem and leaf diagram for these data. [3 marks]
2. Find the median and quartiles for these data. [4 marks]
3. Represent these data with a boxplot. [3 marks]

Tahira played in the same 30 games and her lowest and highest points total in a game were 19 and 41 respectively. The quartiles for Tahira were 27, 31 and 35 respectively.

1. Using the same scale draw a boxplot for Tahira's points totals. [2 marks]
2. Compare and contrast the number of points scored per game by Jane and Tahira. [3 marks]

A College offers evening classes in GCSE Mathematics and English. In order to assess which age groups were reluctant to use the classes, the College collected data on the age in completed years of those currently attending each course. The results are shown in this back-to-back stem and leaf diagram. \includegraphics{figure_4} Key: \(1 | 3 | 2\) means age 31 doing Mathematics and age 32 doing English

1. Find the median and quartiles of the age in completed years of those attending the Mathematics classes. [4 marks]
2. On graph paper, draw a box plot representing the data for the Mathematics class. [3 marks]

The median and quartiles of the age in completed years of those attending the English classes are 25, 41 and 57 years respectively.

1. Draw a box plot representing the data for the English class using the same scale as for the data from the Mathematics class. [3 marks]
2. Using your box plots, compare and contrast the ages of those taking each class. [4 marks]

The stem-and-leaf diagram shows the heights, in centimetres, of 15 plants. $\begin{array}{l|l} 0 & 2
1 & 0
2 & 4
3 & 0\ 2\ 4\ 9
4 & 1\ 2\ 4\ 7\ 9
5 & 3\ 7
6 & 2 \end{array}$ Key: \(2 | 5\) means 25 cm.

1. Draw a box-and-whisker plot to illustrate the data. [4]

A statistician intends to analyse the data, but wants to ignore any outliers before doing so.

1. Discuss briefly whether there are any heights in the diagram which the statistician should ignore. [3]