Math Problem Statement

answer after rechecking

Which statement best compares the standard deviations of the numbers of glue sticks brought in by each student for these two classes, based on the dot plots provided for Class A and Class B?

Solution

To analyze the problem, we need to compare the standard deviations of the data from Class A and Class B based on the given dot plots.

Step-by-step process:

  1. Class A:

    • The number of glue sticks brought by students ranges from 1 to 7.
    • The dot plot shows a larger spread, with fewer glue sticks at the lower values and gradually increasing towards the higher values.
  2. Class B:

    • The number of glue sticks brought ranges from 14 to 20.
    • The data points seem to be concentrated towards the middle, around 17 or 18 glue sticks, indicating less variability than Class A.

Observations:

  • Class A has a wider spread of values (from 1 to 7), indicating a greater variability or dispersion in the number of glue sticks brought by students.
  • Class B, while spread from 14 to 20, has a more concentrated distribution, with many dots around the middle values, suggesting a lower variability.

Standard deviation:

The standard deviation is a measure of the spread or dispersion of a data set. Since Class A shows a wider spread than Class B, it would have a higher standard deviation.

Conclusion:

  • The standard deviation of the number of glue sticks brought in by students in Class A is greater than that of Class B.

Thus, the correct answer is C.

Would you like more details, or have any other questions?

Here are 5 related questions to explore:

  1. What is the formula for calculating standard deviation?
  2. How does the range of a data set affect its standard deviation?
  3. Can two data sets with the same range have different standard deviations?
  4. How would removing an outlier affect the standard deviation of a data set?
  5. What other measures of variability are used besides standard deviation?

Tip: A wider range of values typically increases the standard deviation, but the distribution of those values matters just as much.

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Math Problem Analysis

Mathematical Concepts

Statistics
Standard Deviation
Variability

Formulas

Standard deviation formula: σ = sqrt((Σ(xi - μ)^2) / N)

Theorems

Standard Deviation Definition

Suitable Grade Level

Grades 10-12