Math Problem Statement

17 17 18 18 19 19 20 20 20 21 21 21 21 22 23 24 26 28 29 29 30 32 32 32 33 35 37 38 40 52 Using the data of all the ages of everyone in the class, find the following: a. Mean

b. Median

c. Mode(s)

d. Standard Deviation

e. Range

f. Q1

g. Q3

h. IQR

i. Make a boxplot (modified boxplot that shows outliers, if any)

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j. Is the data symmetric or skewed? If skewed, which way?

symmetric right-skewed left- skewed

Solution

Here are the results based on the data of ages provided:

a. Mean:

The mean age is approximately 26.47.

b. Median:

The median age is 23.5.

c. Mode(s):

The mode (most frequent age) is 21.

d. Standard Deviation:

The standard deviation is approximately 8.23.

e. Range:

The range is 35 (52 - 17).

f. Q1 (First Quartile):

Q1 (25th percentile) is 20.0.

g. Q3 (Third Quartile):

Q3 (75th percentile) is 32.0.

h. IQR (Interquartile Range):

The IQR is 12.0 (32 - 20).

i. Boxplot:

A boxplot has been generated showing the data distribution, including potential outliers.

j. Symmetry/Skewness:

The data is right-skewed (mean > median), meaning there are more values on the lower end with a few larger values pulling the mean upwards.

Would you like more details or have any questions?

Here are 5 follow-up questions:

  1. How is the standard deviation affected by extreme values (outliers)?
  2. What does the interquartile range tell us about the spread of the middle 50% of the data?
  3. How would removing outliers impact the skewness of the data?
  4. What can the mode tell us about the typical age in the dataset?
  5. How does the range of a dataset differ from the interquartile range?

Tip: The standard deviation helps understand how much individual data points deviate from the mean on average.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency
Measures of Spread
Data Distribution

Formulas

Mean: (Sum of all values) / (Number of values)
Median: Middle value in sorted data
Mode: Most frequent value
Standard Deviation: sqrt((Σ(xi - x̄)²) / N)
Range: Max value - Min value
Quartiles: Q1 and Q3 (values at 25th and 75th percentiles)
IQR: Q3 - Q1

Theorems

Empirical Rule for normal distribution
Chebyshev's inequality for general distributions

Suitable Grade Level

Grades 10-12