Math Problem Statement

help solve this

Find range, mean, median, mode, and standard deviation of the following sample set: 12, 45, 69, 23, 4, 36, 16, 21, 23, 47, 13, 22, 40, 12, 23, 10, 25

Solution

Here are the calculated values for the given sample set:

  • Range: 65 (Difference between the maximum value 69 and minimum value 4)
  • Mean: 25.94 (Average of the data)
  • Median: 23 (Middle value when the data is ordered)
  • Mode: 23 (Most frequent value)
  • Standard Deviation: 16.62 (A measure of the dispersion of the data)

Would you like further details or explanations about any of these calculations?

Here are some related questions to deepen your understanding:

  1. How is the standard deviation different from the variance?
  2. Why is the mode important when the data is not normally distributed?
  3. What is the difference between sample and population standard deviation?
  4. How does the mean differ from the median in a skewed distribution?
  5. Can the mode be more than one value? Why?

Tip: Always check if the data is normally distributed when interpreting the mean and standard deviation, as they are sensitive to outliers.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Statistics
Data Analysis

Formulas

Range = max(data) - min(data)
Mean = sum(data) / number of data points
Median: Middle value in ordered data set
Mode: Most frequent value
Standard Deviation = sqrt(sum((x_i - mean)^2) / (n - 1))

Theorems

None directly, but involves measures of central tendency and spread

Suitable Grade Level

Grades 9-12

Related Recommendation

Find Mean, Median, Midrange, Range, and Standard Deviation for a Data Set

Statistical Analysis of a Number Set: Mean, Median, Mode, Range

Mean, Median, Mode, and Range Calculation for a Set of Observations

Analyzing a Data Set: Mean, Median, Range, and Standard Deviation

Calculating Mean, Median, Mode, and Range for a Data Set