GED Mathematical Reasoning: Frequency Tables

  • A frequency table is another way of summarizing data. A frequency table depicts the number of times a data value occurs.
  • A frequency table can have several columns depending on the data. The first column is designated for intervals. The amount of intervals is determined by the range in data values. Another column is designated for tallied results. This is where you tally the number of times you see a data value from each interval. Sometimes number values will be used instead of tallies.

 

Example 1

A high school snack bar manager asks her employee to keep a record of the snacks purchased after school one afternoon. She then recorded the data to make the frequency table shown below. Pizza slices accounted for what percent of snack bar purchases that day?

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The frequency table given in example one is titled “Snack Bar – Snack Preferences” where each tally mark represents a snack purchased one afternoon from the snack bar.

You can picture the scenario in your mind… When a bag of chips is purchased, the snack bar worker makes a tally next to the category “bag of chips.” When a hot dog is purchased, a tally is made next to the hot dog category and so on.

So based on the frequency table we can count the tallies in each category to see that 8 bags of chips were purchased, 16 candy bars were purchased, 10 hot dogs were purchased, 4 hamburgers were purchased, and 22 slices of pizza were purchased.

The total number of tallies is 60, meaning that the total number of snacks purchased equaled 60.

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To determine what percent of the purchases were for pizza slices, we will divide the ‘part’ by the ‘whole.’

The ‘part’ is equal to the number of pizza slices purchased, which was 22. The ‘whole’ is equal to the total number of snacks purchased, which was 60.

Percent = \frac{Part}{Whole} = \frac{Pizza\, Slices}{Total\, Number\, of\, Snacks} = \frac{22}{60}

We can use a calculator to find the rate by dividing 22 by 60. The result is: 0.366666… Let’s round this decimal to the nearest hundredths place, making it:  0.37

Percent = \frac{Part}{Whole} = \frac{Pizza\, Slices}{Total\, Number\, of\, Snacks} = \frac{22}{60} = 0.37

And finally, we’ll change the decimal 0.37 into a percent by moving the decimal point two places to the right and adding a percent sign.

0.37 \rightarrow 37\%

Therefore, pizza slices accounted for about 37% of the snacks purchased that afternoon.

 

Example 2

Mr. Wade surveyed his students regarding the amount of time each spent studying for a recent math exam. He then recorded the data to make the grouped frequency table shown below. What percent of the students studied one hour or less?

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The frequency table in example two is titled “Minutes Spent Studying for Math Exam” where each tally mark represents a student in Mr. Wade’s class. Based on the grouped frequency table we can count the tallies in each interval to see that 6 students studied zero to 30 minutes, 11 students studied 31 to 60 minutes and so on. The total number of tallies is 33, which is the total number of students in Mr. Wade’s class.

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To determine the percent of the students that studied one hour or less, we will divide the ‘part’ by the ‘whole’.

The ‘part’ is equal to the number of students that studied one hour or less. Since one hour is equal to 60 minutes, the number of students that studied one hour or less is represented by the tallies for the intervals zero to 30 and 31 to 60. This means 17 students studied one hour or less, making the numerator of our fraction 17. The ‘whole’ is equal to the total number of students in the class, which was 33.

percent = \frac{part}{whole} = \frac{number\, of\, students\, who\, studied\, one\, hour\, or\, less}{total\, number\, of\, students} = \frac{17}{33}

We can use a calculator to solve for the rate by dividing 17 by 33. The result is: 0.515151… Let’s round this decimal to the nearest hundredths place, making it: 0.52. Finally, we’ll change the decimal 0.52 into a percent by moving the decimal point two places to the right and adding a percent sign. Therefore, the percentage of students in Mr. Wade’s class who studied one hour or less was about 52%

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