Math Problem Statement

1 2 3 4 5 1 2 3 4 5 Number of children Frequency [Graphs generated by this script: setBorder(47,40,20,5); initPicture(0,4.5,0,5);axes(1000,1,1,1000,1); fill="blue"; stroke="black";line([1,-0.1],[1,0.1]); text([1,0],"1","below");line([2,-0.1],[2,0.1]); text([2,0],"2","below");line([3,-0.1],[3,0.1]); text([3,0],"3","below");line([4,-0.1],[4,0.1]); text([4,0],"4","below");line([5,-0.1],[5,0.1]); text([5,0],"5","below");textabs([165,0],"Number of children","above");textabs([0,115],"Frequency","right",90);rect([0.5,0],[1.5,3]);rect([1.5,0],[2.5,2]);rect([2.5,0],[3.5,4]);rect([3.5,0],[4.5,5]);]

A survey asked how many children people have. The survey results are given in the histogram above. Find the relative frequency of people who have 2 children.

Solution

To find the relative frequency of people who have 2 children, we need two pieces of information from the histogram:

  1. The frequency of people with 2 children.
  2. The total number of people surveyed.

Step 1: Find the frequency of people who have 2 children.

From the histogram:

  • The bar representing people with 2 children has a height of 2. Therefore, the frequency of people who have 2 children is 2.

Step 2: Find the total number of people surveyed.

From the histogram, we sum the frequencies of all the bars:

  • Frequency for 1 child = 3
  • Frequency for 2 children = 2
  • Frequency for 3 children = 4
  • Frequency for 4 children = 5

So, the total number of people surveyed is: 3+2+4+5=143 + 2 + 4 + 5 = 14

Step 3: Calculate the relative frequency.

The relative frequency is calculated by dividing the frequency of people with 2 children by the total number of people surveyed: Relative frequency=Frequency of 2 childrenTotal frequency=214=170.1429\text{Relative frequency} = \frac{\text{Frequency of 2 children}}{\text{Total frequency}} = \frac{2}{14} = \frac{1}{7} \approx 0.1429

Thus, the relative frequency of people who have 2 children is approximately 0.1429, or 14.29%.

Would you like further details on how relative frequencies work or any other aspect of this question? Here are 5 related questions to explore:

  1. What is the relative frequency for people who have 3 children?
  2. How is a relative frequency different from an absolute frequency?
  3. How would the relative frequency change if more people with 2 children were surveyed?
  4. How can cumulative frequency be calculated from the given data?
  5. What is the probability interpretation of relative frequency in statistics?

Tip: In a histogram, the relative frequency is the proportion of the total data set that each bar represents.

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Math Problem Analysis

Mathematical Concepts

Statistics
Relative Frequency
Histogram Interpretation

Formulas

Relative Frequency = Frequency of Event / Total Frequency

Theorems

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Suitable Grade Level

Grades 6-8