Agroup of students were given a spelling test. the table shows their marks.
mark 6,7,8,9,10 frequency 5,4,7,10,4
work out the range of the marks,
how many students are in the group
work out the mean mark of the group

Range

The range measures the spread of the dataset by calculating the difference between the largest and the smallest element. In your case, marks range from 6 to 10, so the range is 10-6=4.

How many students

The frequency tells you how many students got each mark. So, we know that 5 students got a mark of 6, 4 students got a mark of 7, 7 students got a mark of 8, 10 students got a mark of 9, 4 students got a mark of 10.

This implies that, in total, we have

students.

Mean

The mean is given by the sum of the marks, divided by the number of students. We already observed how many students got each mark, so the sum of all marks will be a weighted sum, where each mark counts once per student:

Now we divide this sum by the number of students to get

So, the average mark is about 8.

The range is the difference between the highest and the least mark.

(a) Range

From the question, the highest and the least marks are:

So, the range is:

(b) The students in the group

This is the sum of the frequency of each mark group

So, we have:

Hence, the number of students in the group is 30

(c) The mean mark

This is calculated as:

So, we have:

Hence, the mean mark is 8.13

Read more about mean, frequencies and range at:

link

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