Math Problem Statement
The scores on the most recent quiz in a history class are: 27, 28, 30, 32, 34, 38, 41, 42, 43, 46, 53, 56, 62. The teacher described the distribution of scores as skewed to the left. Check the teachers work by:
Find the five number summary of the data and list the values. Drawing a boxplot of the data and uploading the image in your discussion post (you can draw this by hand or use a computer program). Is the teacher correct? Explain in at least one complete sentence.
Solution
The five-number summary of the quiz scores is as follows:
- Minimum: 27
- Q1 (25th percentile): 32.0
- Median: 41.0
- Q3 (75th percentile): 46.0
- Maximum: 62
You can also view the boxplot of the data here.
Is the teacher correct?
The teacher mentioned that the distribution is skewed to the left, but based on the boxplot and the five-number summary, the data seems to be skewed to the right, since the longer tail is towards the higher scores. This suggests the teacher might be mistaken.
Would you like any more details or explanations?
Related questions:
- How is skewness determined from a boxplot?
- Can you explain how outliers are identified in a boxplot?
- What is the interquartile range, and how does it help in understanding data spread?
- How would the boxplot change if one of the scores was much higher than 62?
- How does the median compare to the mean in skewed distributions?
Tip: In a skewed right (positively skewed) distribution, the mean is usually greater than the median.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Five-Number Summary
Boxplot
Data Distribution
Skewness
Formulas
Five-Number Summary: Minimum, Q1 (25th percentile), Median, Q3 (75th percentile), Maximum
Theorems
Skewness in Data Distribution
Suitable Grade Level
Grades 9-12