Descriptive Statistics - Examples & Applications

Solved Problems

A civil engineer measures the compressive strength (in MPa) of 5 concrete cylinder samples:

\{ 25, 28, 24, 30, 28 \}

Calculate the sample mean, median, mode, variance, and standard deviation.

0 of 1 Steps Completed

Find the interquartile range (IQR) for the following set of soil moisture contents (in %):

\{ 12, 15, 14, 18, 22, 16, 15 \}

0 of 1 Steps Completed

A traffic engineer studies the speeds of vehicles on a highway. The frequency distribution of speeds (in km/h) is recorded below:

Calculate the approximate mean speed of the vehicles.

0 of 4 Steps Completed

The mean curing time for a specific type of epoxy resin is

45

hours, with a standard deviation of

3

hours. Using Chebyshev's Theorem, determine the minimum percentage of epoxy samples that will cure between

37.5

and

52.5

hours.

0 of 3 Steps Completed

Key Takeaways

Central Tendency: Describes the center of the data (Mean, Median, Mode).
Dispersion: Describes the spread of the data (Range, Variance, Standard Deviation).
Variance vs. Standard Deviation: Variance is in squared units; Standard Deviation is in original units.
Sample vs. Population: Use $n-1$ for sample variance to correct for bias.
Grouped Data: Midpoints act as representatives for the entire class when calculating mean for grouped frequency distributions.
Chebyshev's Theorem: Provides a guaranteed minimum percentage of data within $k$ standard deviations, regardless of the distribution's shape.