Initial Publication Date: August 11, 2023

# Introductory Statistics - Practice Problems

## Solving Earth science problems with mean, median, mode, and standard deviation

### Problem 1: Strike and dip measurements along an outcrop (Calculating a Mean)

The strike and dip of a bedrock unit describe the orientation and inclination.

As a structural geologist, you are tasked with producing a geologic map of an area. You track a long outcrop of shale and take strike and dip measurements in 8 locations. Below is the table from your field notebook. Find the mean strike and the mean dip of the measurements.

 Strike (°) Dip (°) 015 34 017 39 020 31 016 33 021 37 018 32 020 38 014 33

### Problem 2: Most common hurricane categories (find the mode)

Hurricanes are classified on a scale of 1-5 based on the Saffir-Simpson Hurricane Wind scale. A "major" hurricane is one that is a category 3, 4, or 5.

What is the most common major hurricane type (category 3, 4, or 5) to have made landfall in Florida since 1851?

### Problem 3: Snow Water Equivalent values in the Northern Gallatin Range, Montana (Calculate mean, standard deviation, median, and interpret)

Snow Water Equivalent (SWE) is a measure of precipitation derived from snow. It is the height of water per unit area if the snow were melted. An automated network of snow monitoring stations, called SNOTEL stations, record SWE in the western United States.

Below are the peak SWE values from the Lick Creek SNOTEL station in Montana for the years 2004-2023.

• Part 1: Calculate the mean peak SWE for the years 2004-2023
• Part 2: Calculate the standard deviation of the SWE data.
• Part 3: Calculate the median and mode for the twenty years of SWE data.
• Part 4: Interpret your findings. What does the standard deviation tell us about the spread of the SWE data? Would mean or median be a better measure of the typical peak SWE for these years, mean or median? Why?

 Water Year Peak SWE (in.) 2023 14.5 2022 11.9 2021 11.5 2020 14.2 2019 11.1 2018 15.5 2017 8.9 2016 10.5 2015 8.8 2014 18.5 2013 11.8 2012 11.0 2011 18.8 2010 10.9 2009 14.0 2008 14.1 2007 11.9 2006 10.1 2005 9.6 2004 9.9

Part 1: Calculate the mean peak SWE.

Part 2: Calculate the standard deviation of the SWE data.

Part 3: Calculate the median SWE.

Part 4: Interpret your findings. What does the standard deviation tell us about the spread of the SWE data? Would mean or median be a better measure of the central tendency of the SWE data?

### Problem 4: Permafrost thaw (Calculate mean, median, and mode)

Permafrost thaw is an issue of great concern in the arctic and subarctic regions of the world. The uppermost layer of soil, called the "active layer," thaws in the summers, but the permafrost below stays frozen. The thickness of the active layer has been increasing with climate warming, as more permafrost thaws and becomes part of the active layer.

Your job is to monitor the depth of the active layer at a set of monitoring plots. Each plot (100m x 100m) contains 12 measurement sites equipped with frost tubes and soil temperature cables. During peak summer each year, you obtain measurements of the thickness of the active layer to add to a long-term dataset.  Your values of active layer thicknesses at the plot in the most recent year are as follows.

Part 1: Calculate the mean. Part 2: calculate the standard deviation. Part 3: Calculate the median of the values. Part 4: Do you think mean or median is a better measurement of the central tendency of the data in this case?

 Site Active layer thickness (cm) 1 30 2 45 3 120 4 25 5 63 6 12 7 54 8 68 9 55 10 39 11 46 12 67

Part 1: Calculate the mean of the data

Part 2: Calculate the standard deviation

Part 3: Calculate the median of the data

Part 4: Which is a more appropriate statistic for the active layer data, mean or median?

## Next steps

If you feel comfortable with this topic, you can go on to the assessment.

Or you can go back to the Introductory Statistics explanation page.