Using the given data for school performance, complete the frequency table.
So presumably, these data points relate to individual students in a class. And their school performance has been estimated to be either very weak, weak, pass, good, very good, or excellent. We’re asked to complete the frequency table. Which means, we need to calculate the frequency in each category. How many students are in it.
I’m going to answer this question by first creating a tally chart. I’ll put one tally mark in each column, each time that category appears. The first piece of data is: weak. So I put one tally mark in the column for “weak”. I’ll then cross this piece of data out because I know it’s been dealt with. The next piece of data is: good. So I put one tally mark in this column. The third piece of data is: weak. So I put a second tally mark in the column for “weak”. I’m now going to continue through the remainder of the data.
I’ve now added the first 15 pieces of data to my tally chart. And I’m going to pause at this point because the next piece of data is: weak. If I look at the column for “weak”, I can see the that there’re already four tally marks in this column. To represent the fifth person, I put a diagonal line through these for tally marks. And this group now indicates five people. I’ll now add the remaining four pieces of data to my tally chart. Now that I’ve completed the tally chart, I just need to add up the tally marks in each column in order to determine the frequencies.
In the “Very weak” column, there are four individual tally marks. So the frequency is four. In the “weak” column, there is one set of four tally marks with a diagonal line through it. So the frequency in this column is five. There are no tally marks in the “Pass” column. So the frequency is zero. For “good”, there are three individual tally marks. The frequency is three. In the “Very Good” column, there is one set of four tally marks with a diagonal line through it, representing five people, and one individual tally mark. Therefore, the total frequency for “Very good” is six. In the “Excellent” column, there are two individual tally marks. The frequency is two.
So we’ve completed the frequency table. Now, it’ll be sensible at this point to check the total, to make sure we haven’t missed any of the data out. The sum of the six frequencies is 20. If we look back at the data we were given for school performance, there are five columns and four rows. So there were 20 data pieces here. Therefore, we know that we haven’t missed any of the data when completing our tally chart.
The values in the completed frequency table are as follows: four, five, zero, three, six, two.