Standard Deviation Worksheet

Lesson 4-4STANDARD DEVIATION
The range is a limited measure of variation because it ignores all the data except the highest
and lowest values. If most of the values are similar, but there is just one unusually high value,
the range will make it look like there is a lot more variation than there actually is. For this
reason, we will study standard deviation, which is a more reliable (and commonly used)
measure of variation.
Standard deviation is a little tricky to compute. We are not going to study all the small steps
but will instead use technology to find the standard deviation. Most importantly, we want to
understand its meaning.
Interpretation of Standard Deviation:
• The standard deviation should be thought of as the average distance from each data
point to the mean.
• A standard deviation that is large tells us that the data values vary widely from the mean.
• A smaller standard deviation means that most data values are clustered closely to the
mean.
Rather than use a formula for the Standard Deviation, we are going to use Desmos. Once
you open the Desmos Scientific calculator, follow these steps:
• Click on the ‘func’ tab in the calculator
• Click on the ‘stdev’ button
• Type each data value separated by a comma
• Close the parentheses
• Hit enter and you will get the Standard Deviation
You can also use Desmos to find the Mean (or average) of a set of data. Once you open the
Desmos Scientific calculator, follow these steps:
• Click on the ‘func’ tab in the calculator
• Click on the ‘mean’ button
• Type each data value separated by a comma
• Close the parentheses
• Hit enter and you will get the Mean
1. The table below shows the number of arrests in the US for possession of marijuana, in
thousands, for the years from 2008 to 2017. All data was gathered from the annual
Uniform Crime Report published by the FBI.
Year
Arrests
(Thousands)
Distance
from 𝒙𝒙
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
620
620
614
541
543
503
516
575
653
599
a. Find the mean and standard deviation for the number of arrests.
b. Complete the table by finding the distance of each data value from the mean; that
distance is always positive. Then compute the average distance from the data to the
mean 𝒙𝒙. How does it compare to the standard deviation?
c. What does the standard deviation tell you about the variation in the data?
2. For each of the following, identify the data set that is likely to have a larger standard
deviation. Explain your reasoning.
a. Data set 1: 40-yard dash times for running backs in the National Football League.
Data set 2: 40-yard dash times for every student in this class.
b. Data set 1: Average monthly high temperature in Chicago over the course of one year.
Data set 2: Average monthly high temperature in San Diego over the course of one
year.
c. Data set 1: Weights of all dogs at a golden retriever rescue shelter.
Data set 2: Weights of all dogs in a shelter.
3. A professor has two sections of a class this semester. Class A has a mean score of 74%
with a standard deviation of 3.6% whereas Class B also has a mean score of 74%, but a
standard deviation of 19.2%. Answer true or false for each of the following. Remember, an
answer is false if it is not always true or might not be true in all cases.
a. There were probably some students that took a zero on Class A.
b. There were more students on Class A that had a score close to the average score.
c. More students did better on the exam in Class B
d. The overall highest score by an individual student was in Class B.
e. More students did better in Class A than Class B.
f. Even though the means were the same, the scores on the exam in Class B are more
spread out.