Math Problem Statement

The enrollments at a random selection of independent religiously controlled undergraduate schools are indicated. Find the mean, median, mode, and midrange. Compare the mean and median and what that says about the data.

Solution

Here are the calculated statistics for the college enrollment dataHere are the calculated statistics for the college enrollment

  • Mean (average): 1494.57
  • Median (middle value): 1415.5
  • Mode (most frequent value): 1469
  • Midrange (average of the minimum and maximum values): 1777.5

Comparison of Mean and Median:

The mean (1494.57) is higher than the median (1415.5). This suggests that there may be some higher values in the dataset pulling the mean upwards, indicating a possible right-skew in the data distribution.

Would you like more details on any of these statistics, or have any questions?

Here are five related questions you could explore:

  1. What impact does an outlier have on the mean versus the median?
  2. How is midrange useful compared to other measures like mean and median?
  3. Can a dataset have multiple modes? If so, how is that calculated?
  4. What is the significance of comparing the mean and median in real-world data?
  5. How would changing one value in this dataset affect these measures?

Tip: Median is a robust measure, often more reliable than mean when dealing with skewed distributions or outliers.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency
Measures of Spread

Formulas

Mean = (Sum of all values) / (Number of values)
Median = Middle value when data is ordered
Mode = Most frequent value
Midrange = (Minimum value + Maximum value) / 2

Theorems

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Suitable Grade Level

Grades 9-12