A manufacturing company records the number of defective items produced daily. The data is grouped into class intervals as follows:
Class Interval: 0-5, 5-10, 10-15, 15-20
Frequency: 8, 15, 12, 5
(a) Construct the cumulative frequency distribution table for the given data.
(b) Using linear interpolation, estimate the first quartile (Q1) and the third quartile (Q3) from the cumulative frequency table. Then, calculate the interquartile range (IQR). Show all steps clearly.
Explain each step in your solution.
Question
Construct the cumulative frequency distribution table for the data with the given class intervals and frequencies.
Hint
Hint
Hint
Calculate cumulative frequencies by adding the frequency of each class interval to the sum of frequencies of the preceding intervals.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
| Class Interval |
Frequency |
Cumulative Frequency |
| 0-5 |
8 |
8 |
| 5-10 |
15 |
23 |
| 10-15 |
12 |
35 |
| 15-20 |
5 |
40 |
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Answer Explanation
Answer Explanation
Question
Using linear interpolation and the cumulative frequency table from part (a), estimate the first quartile (Q1) and the third quartile (Q3). Calculate the interquartile range (IQR).
Hint
Hint
Hint
To estimate Q1 and Q3, first find their positions in the data set. Then, identify the class intervals containing Q1 and Q3 using the cumulative frequencies. Apply the linear interpolation formula: \(Q = L + \frac{\frac{kN}{4} – CF_{prev}}{f} \times w\), where k=1 for Q1, k=3 for Q3, N is total frequency, \(CF_{prev}\) is the cumulative frequency before the quartile class, f is the frequency of the quartile class, and w is the class width.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
Q1 ≈ 5.67, Q3 ≈ 12.92, IQR ≈ 7.25
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