Draw histogram from frequency table

4 The times taken, \(t\) seconds, by 1140 people to solve a puzzle are summarised in the table.

1. On the grid, draw a histogram to illustrate this information.
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2. Calculate an estimate of the mean of \(t\).

2 The floor areas, \(x \mathrm {~m} ^ { 2 }\), of 20 factories are as follows. Represent these data by a histogram on graph paper, using intervals $$0 \leqslant x < 500,500 \leqslant x < 1000,1000 \leqslant x < 2000,2000 \leqslant x < 3000,3000 \leqslant x < 4000 .$$

5 The number of people a football stadium can hold is called the 'capacity'. The capacities of 130 football stadiums in the UK, to the nearest thousand, are summarised in the table.

1. On graph paper, draw a histogram to represent this information. Use a scale of 2 cm for a capacity of 10000 on the horizontal axis.
2. Calculate an estimate of the mean capacity of these 130 stadiums.
3. Find which class in the table contains the median and which contains the lower quartile.

1 The number of minutes of recorded music on a sample of 100 CDs is summarised below.

1. Illustrate the data by means of a histogram.
2. Identify two features of the distribution.

3 The times taken for 480 university students to travel from their accommodation to lectures are summarised below.

1. Illustrate these data by means of a histogram.
2. Identify the type of skewness of the distribution.

2 The engine sizes \(x \mathrm {~cm} ^ { 3 }\) of a sample of 80 cars are summarised in the table below.

1. Draw a histogram to illustrate the distribution.
2. A student claims that the midrange is \(2750 \mathrm {~cm} ^ { 3 }\). Discuss briefly whether he is likely to be correct.
3. Calculate estimates of the mean and standard deviation of the engine sizes. Explain why your answers are only estimates.
4. Hence investigate whether there are any outliers in the sample.
5. A vehicle duty of \(\pounds 1000\) is proposed for all new cars with engine size greater than \(2000 \mathrm {~cm} ^ { 3 }\). Assuming that this sample of cars is representative of all new cars in Britain and that there are 2.5 million new cars registered in Britain each year, calculate an estimate of the total amount of money that this vehicle duty would raise in one year.
6. Why in practice might your estimate in part (v) turn out to be too high?

1. The total amount of time a secretary spent on the telephone in a working day was recorded to the nearest minute. The data collected over 40 days are summarised in the table below.

Draw a histogram to illustrate these data

1. 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.
2. Find the three quartiles for the distribution.
3. On graph paper construct a box plot for the data, showing your scale and clearly indicating any outliers.

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

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.
2. Find the three quartiles for this data.
3. On graph paper, draw a box plot for the data.
4. Describe the skewness of the distribution.