Envision Math 2.0: Grade 8, Volume 1
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4. Interpret Two-Way Frequency Tables
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Exercise 8 Page 235

Use the already filled slots in the table to calculate the values in other slots. Remember that the last row and column represents the totals.

two-way frequency table
Practice makes perfect

We asked 203 of our classmates how they feel about the school year being made longer. To complete the two-way frequency table showing the results of the survey, we need to recognize that the last row and the last column show totals.

two-way frequency table

From the table above, we know that of the students who voted sad face, 25 were 6th graders, 2 were 7th graders, and 24 were 8th graders. With this information, we can find the number of all students who voted sad face.

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Also, of the 47 students who voted indifferent, 14 were 6th graders and 21 were 8th graders. With this information, we can find the number of 7th graders who voted indifferent.

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Moreover, of the 203 students who voted took part in the survey, 72 were 6th graders and 73 were 8th graders. With this information, we can find the number of 7th graders who took part in the survey.

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Let's write the given and the newly obtained information in our table.

two-way frequency table

Let's clear the table and recolor the values to help us complete the rest of the table!

two-way frequency table

From the table above, we know that of the 58 7th graders, 1 voted crying face, 2 voted sad face, 12 voted indifferent, and 8 voted grinning face. With this information, we can find the number of 7th graders who voted happy face.

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Also, of the 203 students who took part in the survey, 44 voted crying face, 51 voted sad face, 47 voted indifferent, and 42 voted happy face. With this information, we can find the number of students who voted grinning face.

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Let's write the given and the newly obtained information in our table.

two-way frequency table

Let's once again clear the table and recolor the values to help us complete the rest of the table!

two-way frequency table

From the table above, we know that of the 42 students who voted happy face, 35 were 7th graders, and 3 were 8th graders. With this information, we can find the number of 6th graders who voted happy face.

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Also, we know that of the 19 students who voted grinning face, 4 were 6th graders, and 8 were 7th graders. With this information, we can find the number of 8th graders who voted grinning face.

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Let's write the given and the newly obtained information in our table.

two-way frequency table

For the last time, we will clear the table and recolor the values to help us complete the table!

two-way frequency table

From the table above, we know that of the 72 6th graders, 25 voted sad face, 14 voted indifferent, 4 voted happy face, and 4 voted grinning face. With this information, we can find the number of 6th graders who voted crying face.

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Also, of the 73 8th graders, 24 voted sad face, 21 voted indifferent, 3 voted happy face, and 7 voted grinning face. With this information, we can find the number of 8th graders who voted crying face.

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Finally, let's complete our table!

two-way frequency table