Math Problem Statement
the daily online newspaper America at a Glance has just published an article detailing a study of 50 students who completed preparation programs for a nationwide standardized test. The following histogram, which summarizes the mathematics test score information for the 50 sampled students, appeared in the article. Relative frequency: 0.14,0.22,0.32,0.24,0.08 Mathematics test scores:550,600,650,700,750,800 based on the histogram, find the proportion of mathematics test scores in the sample that are less than 650. Write your answer as a decimal, and do not round your answer
Solution
To find the proportion of mathematics test scores in the sample that are less than 650, we need to add up the relative frequencies of the scores that are less than 650.
From the given data, the scores that are less than 650 are:
- 550
- 600
We are also given the corresponding relative frequencies for these scores:
- Relative frequency for 550 = 0.14
- Relative frequency for 600 = 0.22
Now, we can simply add these relative frequencies:
So, the proportion of mathematics test scores that are less than 650 is 0.36.
Would you like any further explanation or details? Here are some related questions to consider:
- What is the proportion of students who scored between 650 and 700?
- How does the relative frequency relate to the actual number of students in each score range?
- What does the shape of the histogram suggest about the distribution of the test scores?
- If there were 1000 students in the sample, how many would you expect to score less than 650?
- How do histograms help in understanding data distributions and trends?
Tip: Histograms are a great visual tool for quickly assessing the distribution of data, as they show the frequency of data within different intervals or "bins."
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Math Problem Analysis
Mathematical Concepts
Probability
Relative Frequency
Statistics
Data Interpretation
Formulas
Sum of relative frequencies for specified categories
Theorems
Basic properties of relative frequency in histograms
Suitable Grade Level
Grades 6-8
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