Mathematics

Mathematics

Problem

The table shows the petrol sales in one day by a number of city service stations.
Amount of petrol ( PP L)Frequency
2000<P≤30002000 < P \le 30004
3000<P≤40003000 < P \le 40004
4000<P≤50004000 < P \le 50009
5000<P≤60005000 < P \le 600014
6000<P≤70006000 < P \le 700023
7000<P≤80007000 < P \le 800016
a. How many service stations were involved in the survey? b. Estimate the total amount of petrol sold for the day by the service stations. c. Estimate the mean amount of petrol sold for the day. d. Find the modal class for this distribution. Explain your answer.
Intuitive explanation

This is a grouped frequency distribution problem where you need to find a typical value or position within the data. The key insight is that with continuous data grouped into intervals, you can't just count—you need to use the cumulative frequencies to locate where the median (or other percentiles) falls, then estimate its exact position within that interval using linear interpolation.

Intuitive explanation

This is a grouped frequency distribution problem where you need to find a typical value or position within the data. The key insight is that with continuous data grouped into intervals, you can't just count—you need to use the cumulative frequencies to locate where the median (or other percentiles) falls, then estimate its exact position within that interval using linear interpolation.

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