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# The following frequency distribution displays the scores on a math test.
Find the class boundaries of the scores interval 50 - 59.
| Scores | Number of Students |
| --- | --- |
| $50 - 1$ | 2 |
| $60 - 1$ | 4 |
| $70 - 1$ | 6 |
| $80 - 1$ | 15 |
| $90 - 1$ | 5 |
a) $49.5 - 59.1$ b) $49 - 1$ c) $50.5 - 58.1$ d) $49.9 - 59.1$
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Answer
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Step 1:I'll solve this step by step using the class boundaries concept.
Step 2:: Understand Class Boundaries
Class boundaries are the real limits of a class interval. They are calculated by finding the midpoints between the upper and lower limits of adjacent classes.
Step 3:: Calculate Lower Class Boundary
For the interval 50 - 59, the lower class boundary is the value that separates this class from the class below it. - Lower adjacent class is not shown, so we use the midpoint between the lower limit of the given class and the lower limit of the next class. - Lower limit of 50 - 59 class is 50 - Lower limit of next class (60 - 69) is 60
Step 4:: Calculate Upper Class Boundary
- Upper limit of 50 - 59 class is 59 - Upper limit of next class (60 - 69) is 69
Step 5:: Compute Boundaries
Lower boundary: $$\frac{50 + 60}{2} = 49.5
Upper boundary: \frac{59 + 69}{2} = 59.5
Step 6:: Verify the Answer Choices
Comparing our calculated boundaries $$49.5-59.5$$ with the given options, we can see this matches option a).
Final Answer
a) 49.5 - 59.5
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