The table of data shows the heights
in centimeters of teachers at a school. Using a frequency table, find the
number of teachers whose heights are greater than or equal to 175 centimeters.
Our first step in this question is
to create a grouped frequency table from the data in the table. The lowest number in the table is
155, which corresponds to a height of 155 centimeters. And the highest number in the table
is 195, which corresponds to a height of 195 centimeters.
The first row of the frequency
table will be the heights of the teachers, and the second row will be the
frequency. We will split the data into five
groups: 155 to 164 centimeters, 165 to 174 centimeters, 175 to 184 centimeters, 185
to 194 centimeters, and 195 to 204 centimeters, noting that it is common practice
for all groups to have the same width.
There are 12 teachers that had a
height between 155 and 164 centimeters. So the first frequency is 12. Next, we see that there are 14
teachers with a height between 165 and 174 centimeters. Nine of the teachers in the table
are in the third group: 175 to 184 centimeters. There are 10 teachers who had a
height between 185 and 194 centimeters. Finally, there are three teachers
who are 195 centimeters tall. And as already mentioned, this is
the largest value in the table. So the final frequency is
At this stage, it is worth checking
we have counted every item of data from the table. 12 plus 14 plus nine plus 10 plus
three equals 48, which means we have counted each value from the table. The question asks us to calculate
how many teachers have a height greater than or equal to 175 centimeters. As such, we need one of the lower
class boundaries to be 175 centimeters. And this corresponds to the last
three columns in the grouped frequency table. We need to add the frequencies of
nine, 10, and three. This is equal to 22.
We can therefore conclude that 22
teachers have a height greater than or equal to 175 centimeters.