Question

Here is a list of the number of books each of the 20 students in a class has. 58 60 48 48 52 48 60 45 48 56 45 48 60 52 52 56 45 60 48 52 a) Indicate the population, the individual, the studied trait and its nature. b) Draw up the table of numbers, frequencies in%, increasing cumulative numbers and increasing cumulative frequencies. c) What is the cumulative strength of the value 56? What does this workforce mean? d) How many students have at most 48 books in their library? e) What is the percentage of students with at least 56 books?

Answer 1

a) We have a class of 20 students and we have a list of the number of books each one has.

As we are considering all the members of the class, and not a sample of it, the population are all the students of the class. Each student has a number of books associated to him.

The studied trait is the number of books owned by the 20 students and its nature is quantitative and discrete.

b) We can start by sorting the data:

45454548484848484852

52525256565860606060

Now, we can group them as:

d) We can find how many students have at most 48 books in their library by looking at the cumulative absolute frequency for 48 (second row of the table).

We can see that 9 students have at most 48 books.

e) As we can see in the table, 65% od the students have less than 56 books (or 52 books at most).

Then, we can calculate the percentage of students that have 56 books or more as the difference between 100% and 65%, which is 100-65 = 35%.

Then, we know that 35% of the students have 56 books or more.

We can check it and see that 7 out of the 20 students have 56 or more books. This represents 7/20 = 0.35 = 35%.