On a weekday, 180 cars travelled past a certain point on a street. The speed of each car was recorded. The cumulative frequency curve below shows the speed, x km/h, and the number of cars whose speed is less than or equal to x km/h.
Given the following frequency table, calculate an estimate of the mean and standard deviation.
| Speed, x (km/h) | \(35<x\leq40\) | \(40<x\leq45\) | \(45<x\leq50\) | \(50<x\leq55\) | \(55<x\leq60\) | \(60<x\leq65\) |
|---|
| Frequency | 16 | 24 | 44 | 60 | 28 | 8 |
Mean (km/h).[1]
Standard deviation (km/h).[1]
Use the curve to estimate
the median speed,[1]
the interquartile range.[1]
The kth percentile speed is 47 km/h. Write down the value of k.[1]
A car is picked at random from the 180 cars. The probability that the car travels more than y km/h is \(7/15\). Find y.[2]
On a weekend, another 180 cars travelled past the same point on the street. The speed of each car was recorded. The box-and-whisker plot below shows the speed of the cars on the weekend.
Draw the box-and-whisker plot on the same grid below to illustrate the speeds of 180 cars on the weekday.[2]
Make one comment comparing the speeds of the cars on the weekday and the weekend.[1]
If the speed of one car was incorrectly recorded and its speed was updated to 90 km/h in the dataset collected on the weekday, which of the value(s) in the five-number summary of the box-and-whisker plot will change? Based on the change(s), describe briefly what will happen to the lengths of the whiskers and the length of the box.[1]
Sally says, “On the weekend, the number of cars travelling at up to 55 km/h is greater than the number travelling between 55 and 68 km/h.” Is she correct? Give a reason for your answer.[1]