Math Problem Statement

I need help with determining the outliers and drawing a boxplot of the following data: 270 210 250 220 230 310 280 250 260 270 260 330 300 240 290 250 270 310 280 300 280 350 280 300 260 250 310 270 360 280 260 230 270 280 290 240 280 290 310 170 190 180 190 170 190 190 110 130 110 220

Solution

Descriptive Statistics:

  • First Quartile (Q1): 222.5
  • Median (Q2): 265.0
  • Third Quartile (Q3): 287.5
  • Interquartile Range (IQR): 65.0

Outlier Calculation:

  • Lower Bound for Outliers: Q11.5×IQR=125.0Q1 - 1.5 \times \text{IQR} = 125.0
  • Upper Bound for Outliers: Q3+1.5×IQR=385.0Q3 + 1.5 \times \text{IQR} = 385.0
  • Outliers: 110, 110

Observations:

  • The outliers in the given data set are 110 (occurs twice).

Boxplot:

The boxplot above visually shows the spread of the data, quartiles, and outliers.

Would you like more details or have any questions?

Further Questions:

  1. How is the Interquartile Range (IQR) useful in identifying outliers?
  2. What are some implications of having outliers in a dataset?
  3. How does the presence of outliers affect the mean and median of the dataset?
  4. What methods can be used to handle outliers in data analysis?
  5. Can you explain the difference between a mild and an extreme outlier?

Tip: Always check the context of your data when handling outliers, as they can sometimes represent important variations rather than errors.

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Math Problem Analysis

Mathematical Concepts

Descriptive Statistics
Outlier Detection
Boxplot

Formulas

First Quartile (Q1)
Third Quartile (Q3)
Interquartile Range (IQR)
Outlier Calculation Formula: Lower Bound = Q1 - 1.5 * IQR, Upper Bound = Q3 + 1.5 * IQR

Theorems

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Suitable Grade Level

Grades 10-12