Question

7 students were weighed. The mode was 70lb with frequency of 5. Range = 60. largest weight was 2x the lowest weight. what is the average of these students.

Answer 1

7 students were weighed. The mode was 70lb with frequency of 5 [mode is that number which has the highest frequency].

Then we have to find the frequencies of other (7 – 5) = 2 students.

Now, range = 60 i.e. (largest weight – lowest weight) = 60.

Also, largest weight was 2 x the lowest weight.

So, (largest weight – lowest weight) = 60.

or, [(2 x the lowest weight) - lowest weight] = 60

or, lowest weight = 60

So, the lowest weight 60lb with frequency of 1.

Now we have to find out the largest weight.

In this problem, largest weight = (2 * the lowest weight) = (2 * 60) = 120 lb

So, the largest weight 120lb with frequency of 1.

The frequency distribution will be

Classmark (xi)	Frequency (fi)	x­i * fi
60	1	60
70	5	350
120	1	120
Total	7	530

As the highlighted cell has the highest frequency (= 5) so the mode is equal to 70.

Now, the average of this dataset is calculated by following formula:

= 530/7

=75.714

Answer: The average of these students is equal to 75.714 lb.