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Speed Analysis 1689C6

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1. **Problem statement:** We have speed data for 50 cars ordered by speed. 4.1 We want to find how many cars drove faster than the speed limit of 50 km/h. 4.2 We want to find the range (variationsbredden) of the dataset, which is the difference between the highest and lowest speeds. 4.3 and 4.4 relate to a new dataset and campaign effect, but we only solve the first question as per instructions. --- 2. **Formula and rules:** - To find how many cars exceed 50 km/h, count all speeds $>50$. - The range is calculated as $$\text{Range} = \text{Max speed} - \text{Min speed}$$ --- 3. **Intermediate work:** - From the graph description, speeds start near 30 km/h and go up to about 75 km/h. - The cars are ordered by speed, so all cars with speed $>50$ are those with speed bars above 50 on the y-axis. 4. **Counting cars faster than 50 km/h:** - The bars increase from about 30 to 75 km/h over 50 cars. - We estimate the number of cars with speed $>50$ by counting bars above 50. - Suppose the first car with speed above 50 is car number $n$. - From the graph, roughly cars from about number 30 to 50 exceed 50 km/h. - So number of cars faster than 50 km/h is approximately $50 - 29 = 21$ cars. 5. **Calculating the range:** - Max speed $\approx 75$ km/h - Min speed $\approx 30$ km/h - Range $$= 75 - 30 = 45$$ km/h --- **Final answers:** - 4.1 Number of cars faster than 50 km/h: **21** - 4.2 Range of speeds: **45 km/h**