Mathematics
Mathematics
Problem
The distribution below shows the number of pages students read in a library session. One frequency is missing. Class interval (pages): 0–10 10–20 20–30 30–40 40–50 Frequency: 6 14 10 4 If the mode of the distribution is pages, answer the following. a. (i) Identify the modal class and state its lower class boundary. b. (ii) Find the missing frequency that satisfies the given mode. c. (iii) After inserting the value of , comment on whether the distribution is unimodal or not, giving a suitable reason.Intuitive explanation
The mode tells you which class interval contains the most data—it's the interval with the highest frequency. Since the mode is 26 pages, it falls in the 20–30 class, meaning that interval must have the highest frequency. Use this constraint to set up an inequality: the frequency of 20–30 must be greater than all other frequencies, including the unknown in the 10–20 class. This gives you the key equation to solve for .
Intuitive explanation
The mode tells you which class interval contains the most data—it's the interval with the highest frequency. Since the mode is 26 pages, it falls in the 20–30 class, meaning that interval must have the highest frequency. Use this constraint to set up an inequality: the frequency of 20–30 must be greater than all other frequencies, including the unknown in the 10–20 class. This gives you the key equation to solve for .