A motorist drives 80km at an average speed of 63km/h which is median and mode
As given, the average speed of the motorist is 63 km/h.
To find if this is also the median and the mode, we need more information about the distribution of speeds.
If we assume that the motorist drove 80km continuously at a constant speed of 63km/h, then the average speed would be 63 km/h, the median speed would be 63 km/h (as there is only one value), and the mode would also be 63 km/h (as it is the most frequently occurring value).
Therefore, if the driver maintained a constant speed of 63 km/h throughout the journey, then 63 km/h is the average, median, and mode speed.
To find out if 63 km/h is both the median and mode, we need to understand the concepts of median and mode.
The median is the middle value in a data set when it is arranged in order. In this case, the data set is the different speeds the motorist drove during the journey. To find the median, we first need to arrange the speeds in ascending or descending order:
80 km (maximum value)
63 km (mode and median)
0 km (minimum value)
Since there are three speeds, the median is the middle value, which is 63 km/h.
The mode is the value that appears most frequently in a data set. In this case, we have three speeds: 80 km/h, 63 km/h, and 0 km/h. As we can see, 63 km/h appears only once, while 80 km/h also appears once. Since both speeds appear only once and have an equal frequency, none of them can be considered the mode.
Therefore, 63 km/h is the median, but it is not the mode in this scenario.