Direct frequency calculation from histogram

1 In the Paris-Roubaix cycling race, there are a number of sections of cobbled road. The lengths of these sections, measured in metres, are illustrated in the histogram.
\includegraphics[max width=\textwidth, alt={}, center]{3aabac69-ead8-40e4-b06f-5e812bb02906-1_897_1398_494_410}

1. Find the number of sections which are between 1000 and 2000 metres in length.
2. Name the type of skewness suggested by the histogram.
3. State the minimum and maximum possible values of the midrange.

1. Ralph records the weights, in grams, of 100 tomatoes. This information is displayed in the histogram below.
   \includegraphics[max width=\textwidth, alt={}, center]{1130517e-33d0-41b1-9303-2d981379954d-02_981_1268_338_274}

Given that 5 of the tomatoes have a weight between 2 and 3 grams,

1. find the number of tomatoes with a weight between 0 and 2 grams. One of the tomatoes is selected at random.
2. Find the probability that it weighs more than 3 grams.
3. Estimate the proportion of the tomatoes with a weight greater than 6.25 grams.
4. Using your answer to part (c), explain whether or not the median is greater than 6.25 grams. Given that the mean weight of these tomatoes is 6.25 grams and using your answer to part (d),
5. describe the skewness of the distribution of the weights of these tomatoes. Give a reason for your answer. Two of these 100 tomatoes are selected at random.
6. Estimate the probability that both tomatoes weigh within 0.75 grams of the mean.

1 In the Paris-Roubaix cycling race, there are a number of sections of cobbled road. The lengths of these sections, measured in metres, are illustrated in the histogram.
\includegraphics[max width=\textwidth, alt={}, center]{854cb8fb-d75d-4854-b3ec-d7edbb21ea7e-2_899_1397_477_372}

1. Find the number of sections which are between 1000 and 2000 metres in length.
2. Name the type of skewness suggested by the histogram.
3. State the minimum and maximum possible values of the midrange.

8 The histogram shows information about the lengths, \(l\) centimetres, of a sample of worms of a certain species.
\includegraphics[max width=\textwidth, alt={}, center]{4c6b7c92-2fc9-4d4f-a199-8e70f34e5eed-5_904_1284_488_242} The number of worms in the sample with lengths in the class \(3 \leqslant l < 4\) is 30 .

1. Find the number of worms in the sample with lengths in the class \(0 \leqslant l < 2\).
2. Find an estimate of the number of worms in the sample with lengths in the range \(4.5 \leqslant l < 5.5\).

3. The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run. \begin{figure}[h] \end{figure} Use the histogram to calculate the number of runners who took between 78.5 and 90.5 minutes to complete the fun run.

5. \begin{figure}[h] \end{figure} A policeman records the speed of the traffic on a busy road with a 30 mph speed limit. He records the speeds of a sample of 450 cars. The histogram in Figure 2 represents the results.

1. Calculate the number of cars that were exceeding the speed limit by at least 5 mph in the sample.
2. Estimate the value of the mean speed of the cars in the sample.
3. Estimate, to 1 decimal place, the value of the median speed of the cars in the sample.
4. Comment on the shape of the distribution. Give a reason for your answer.
5. State, with a reason, whether the estimate of the mean or the median is a better representation of the average speed of the traffic on the road.

5. Figure 2 is a histogram showing the distribution of the time taken in minutes, \(t\), by a group of people to swim 500 m . \begin{figure}[h] \end{figure} a Find the probability that a person chosen at random from the group takes longer than 18 minutes.

1. The histogram shows information about the lengths, \(l\) centimetres, of a sample of worms of a certain species.
\includegraphics[max width=\textwidth, alt={}, center]{a1f6d8ae-699f-496e-9fe8-cda87d73d27c-3_903_1287_379_201} The number of worms in the sample with lengths in the class \(3 \leqslant l < 4\) is 30 .

1. Find the number of worms in the sample with lengths in the class \(0 \leqslant l < 2\).
2. Find an estimate of the number of worms in the sample with lengths in the range \(4.5 \leqslant l < 5.5\).