Two-Way Frequency Table Survey Analysis
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26. In a statewide survey, ninth-grade and tenth-grade students were asked about the number of glasses of water they drink per day. This table shows the results of the survey. All numbers in the table are in thousands.
| | 0-2 Glasses | 3-4 Glasses | 5 or More Glasses | Total |
|---|---|---|---|---|
| Ninth-Grade Students (thousands) | 10 | 13 | | 45 |
| Tenth-Grade Students (thousands) | | 26 | | |
| Total | | | 39 | 107 |
Part A: Complete the two-way frequency table.
Part B: Based on two-way frequency table that you just completed, select all the statements that are correct.
A. The joint frequency of tenth-grade students who drink 0-2 glasses is 19.
B. The total number of students who drink 5 or more glasses is 39.
C. The marginal frequency of tenth-grade students is 45.
D. The joint frequency of ninth-grade students who drink 3-4 glasses is 26.
E. The marginal frequency for students who drink 3-4 glasses is 39.
This question includes visual content: A two-way frequency table titled 'Number of glasses of water drunk per day'. The rows represent students by grade level (Ninth-Grade, Tenth-Grade, and Total). The columns represent the number of glasses (0-2, 3-4, 5 or More, and Total). Some cells are pre-filled: Ninth-grade(0-2)=10, Ninth-grade(3-4)=13, Ninth-grade(Total)=45, Tenth-grade(3-4)=26, Total(5 or More)=39, Total(Total)=107. Empty cells are provided for the student to calculate.
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Step by Step Written Solution
In this problem, we need to complete a two-way frequency table representing a survey of ninth and tenth grade students and their water consumption habits. Then, we will identify which statements about the table are correct. All numbers are in thousands.
Survey Data Analysis
Let's start by looking at the ninth grade row. We know the total is forty-five thousand. To find the missing value for five or more glasses, we subtract the other values in that row from the total.
Next, we look at the total column. The grand total is one hundred and seven thousand. Subtracting the forty-five thousand ninth graders gives us the total number of tenth graders.
Now we can look at the three to four glasses column. The total for this column is the sum of thirteen and twenty-six.
In the five or more glasses column, we have a total of thirty-nine. Since twenty-two are ninth graders, we can find the number of tenth graders by subtracting.
Finally, let's complete the zero to two glasses column. In the tenth grade row, we have a total of sixty-two. Subtracting twenty-six and seventeen gives us nineteen.
The total for the zero to two column is then ten plus nineteen, which is twenty-nine.
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