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3.2 Homework - Describing Data

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A group of adults were asked how many children they have in their families. The bar graph below shows the number of adults who indicated each number of children.

2468Number of ChildrenNumber of Adults012345[Graphs generated by this script: setBorder(49,45,0,10); initPicture(0,19,0,8);axes(1000,2,1,1000,2); fill="blue"; stroke="black";textabs([215,0],"Number of Children","above");textabs([0,170],"Number of Adults","right",90);rect([1,0],[3,2]);text([2,0],"0","below");rect([4,0],[6,8]);text([5,0],"1","below");rect([7,0],[9,5]);text([8,0],"2","below");rect([10,0],[12,2]);text([11,0],"3","below");rect([13,0],[15,1]);text([14,0],"4","below");rect([16,0],[18,1]);text([17,0],"5","below");]

How many adults were questioned?

What percentage of the adults questioned had 0 children? Round to 1 decimal place.

 %

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2468Number of ChildrenNumber of Adults012345

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Solution

Let's break down the information given in the bar graph to solve the two parts of this problem.

Part 1: How many adults were questioned?

The bar graph shows the number of adults who indicated each number of children. By adding up the total number of adults across all categories (from 0 children to 5 children), we can calculate the total number of adults surveyed.

Based on the graph:

  • 0 children: 2 adults
  • 1 child: 8 adults
  • 2 children: 5 adults
  • 3 children: 2 adults
  • 4 children: 1 adult
  • 5 children: 1 adult

The total number of adults is:

2+8+5+2+1+1=19 adults2 + 8 + 5 + 2 + 1 + 1 = 19 \text{ adults}

So, 19 adults were questioned.

Part 2: What percentage of the adults questioned had 0 children?

To calculate the percentage of adults with 0 children, use the formula for percentage:

Percentage=(Number of adults with 0 childrenTotal number of adults)×100\text{Percentage} = \left( \frac{\text{Number of adults with 0 children}}{\text{Total number of adults}} \right) \times 100

Substitute the numbers:

Percentage=(219)×10010.5%\text{Percentage} = \left( \frac{2}{19} \right) \times 100 \approx 10.5\%

Thus, 10.5% of the adults questioned had 0 children.

Would you like more details or have any further questions?

Here are 5 related questions you might consider:

  1. What is the mode of the number of children per adult?
  2. How would the mean number of children per adult be calculated from the data?
  3. What is the median number of children per adult?
  4. How many adults have more than 2 children?
  5. What would happen to the percentage if more adults with 0 children were added?

Tip: Always check if percentages round correctly when using one decimal place.

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Math Problem Analysis

Mathematical Concepts

Statistics
Percentages
Data Interpretation

Formulas

Total Adults = Sum of all adults in each category
Percentage = (Number of adults with 0 children / Total number of adults) * 100

Theorems

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Suitable Grade Level

Grades 5-7