More Less Totals

Question

7th grade 54
8th grade 13
Totals 41 51

A survey asked a random sample of students to estimate if they spent more than or less than an hour a day on social media. Construct a two-way table to summarize the following data:
54 seventh graders were surveyed.
13 eighth graders estimated they spent more than an hour a day on social media.
41 total students estimated they spent more than an hour a day on social media.
51 total students estimated they spent less than an hour a day on social media.
Start by creating a table in which the rows and columns are labeled with headings corresponding to the categories of data being tracked. Enter in the known data.

Answer 1

To construct a two-way table summarizing the survey data, we need to organize the information into rows and columns that represent the grade level and the time spent on social media. The two categories in this case are "More" and "Less" for the time spent on social media, and the rows will represent the grades (7th and 8th).

Here's how the table would look based on the provided information:

| Grade | More | Less | Totals | |--------------|------|------|--------| | 7th grade | 13 | 41 | 54 | | 8th grade | 13 | 38 | 51 | | Totals | 41 | 51 | 92 |

Now let's fill in the missing cells based on the known data:

1. 7th Grade:

   • Total 7th graders surveyed: 54
   • 7th graders estimated spending more than an hour: 13
   • Therefore, 7th graders estimated spending less than an hour:
     • \( 54 - 13 = 41 \)

2. 8th Grade:

   • Total 8th graders surveyed: 13
   • Total students estimating more than an hour: 41
   • Therefore, 8th graders estimating spending more than an hour:
     • The entire group has 41 estimating more.
     • If 13 are from the 8th grade, that leaves:
       • \( 41 - 13 = 28 \) for 7th graders.
   • Adding back, we have:
     • \( 28 (7th) + 13 (8th) = 41 \)

3. Totals:

   • Total students estimating more: 41
   • Total students estimating less: 51
   • Therefore, total students surveyed:
     • \( 41 + 51 = 92 \)

Here's the completed two-way table:

| Grade | More | Less | Totals | |--------------|------|------|--------| | 7th grade | 28 | 26 | 54 | | 8th grade | 13 | 38 | 51 | | Totals | 41 | 51 | 92 |

Final Table:

The final two-way table summarizing the survey data is:

| Grade | More | Less | Totals | |--------------|------|------|--------| | 7th grade | 28 | 26 | 54 | | 8th grade | 13 | 38 | 51 | | Totals | 41 | 51 | 92 |

If you need any further assistance, feel free to ask!