Math Problem Statement
Solution
The image contains four statistical problems involving the calculation of quartiles and percentile ranks based on given data sets. Here are the solutions for each problem:
Problem 1:
The data set represents the number of keyboards assembled at a company for 25 days:
Data Set:
45, 52, 48, 49, 51, 56, 45, 41, 46, 50,
44, 42, 52, 50, 46, 51, 54, 47, 44, 48,
53, 48, 49, 52, 49
a) Calculate the value of the third quartile (Q3).
To find Q3:
- Arrange the data in ascending order.
- Identify Q3, which is the 75th percentile.
Sorted Data:
41, 42, 44, 44, 45, 45, 46, 46, 47, 48,
48, 48, 49, 49, 49, 50, 50, 51, 51, 52,
52, 52, 53, 54, 56
Position of Q3:
Q3 is between the 19th and 20th values, i.e., between 51 and 52.
Q3 Value:
b) Find the percentile rank of 50.
Percentile rank = .
Values below 50: 15 values
Percentile Rank = .
Problem 2:
Data Set: 50, 71, 72, 72, 78, 80, 82, 83, 84, 84, 85, 86, 86, 87, 90, 94, 96, 98, 99.
a) Find the percentile rank for a score of 84.
Number of values below 84: 8
Percentile Rank = .
Problem 3:
Data Set: 72, 74, 76, 78, 80, 84, 84, 85, 86, 88, 89, 91, 94, 96, 98.
a) Find the percentile rank of 89.
Number of values below 89: 10
Percentile Rank = .
Problem 4:
Data Set: 58, 59, 62, 66, 68, 69, 70, 71, 71, 71, 73.
a) Find the percentile rank for score 51.
The score 51 is not present in the data. Assuming you need to find the rank closest to 51:
Values below 51: 0 (because 58 is the lowest).
Percentile Rank = .
Would you like more detailed explanations on these solutions or have any specific questions?
Further Questions:
- How do you determine the first quartile (Q1) in a data set?
- What is the significance of the median in a quartile calculation?
- How can percentile rank be useful in statistical analysis?
- What is the difference between the 25th and 75th percentiles?
- How do you calculate the interquartile range (IQR)?
Tip: Quartiles and percentiles help in understanding data distribution, especially in comparing individual scores against the overall set.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Percentile Ranks
Quartiles
Formulas
Percentile Rank = (number of values below x + 0.5) / total number of values * 100
Q3 = 3(n+1)/4
Theorems
Quartile calculation
Percentile rank determination
Suitable Grade Level
Grades 9-12
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