By Jonny Lupsha, Wondrium Staff Writer
Anthony Fauci said 100 million COVID-19 vaccinations by May is possible, CNN reported. Fauci’s assessment comes after President Biden announced a plan to vaccinate 100 million Americans against COVID-19 in his first 100 days in office. Statistics are the source of Fauci’s estimate.
According to CNN, 2021 may soon be brighter than 2020. “President Biden’s promise to administer 100 million shots in his first 100 days in office will be put to the test,” the article said. “While significantly behind early promises overall, the pace of vaccination has steadily improved over the past five weeks.
“In fact, Dr. Anthony Fauci said it’s likely that vaccine administration will meet—and perhaps even outpace—President Biden’s plan.”
With the rate of vaccinations and their supply changing all the time, how is such an estimate possible? Extracting data from statistics is a worthy endeavor.
What Is Quantitative Data?
Statistics is a branch of mathematics—and science—that involves collecting, analyzing, and interpreting data. One such type is quantitative data, which is always made up of numbers.
“Quantitative data is either discreet or continuous,” said Dr. Talithia Williams, Associate Professor of Mathematics and the Associate Dean for Research and Experiential Learning at Harvey Mudd College, in a lecture for The Great Courses. “Discreet data take on only certain values, certain numerical values like one or three or 17. Continuous data can take on any value along an interval of numbers, and the data is measured on a continuous scale.”
Variables are also a part of data. Dr. Williams said that qualitative variables are often described with words or letters. For example, when measuring hair colors or blood types in a group of people, the specific colors or types are the qualitative variables. They’re also called categorical variables.
Dr. Williams said that statistics is all about using a representative sample taken from a population. How do we know a sample is representative? Representative samples are chosen at random and in a large amount.
“A simple random sample is a subset of the population where each member of the subset has an equal opportunity of being chosen,” she said. “Based on the sample, we try to generalize about the entire population, and that’s known as statistical inference. This is why it’s so important that the sample is representative of the population.”
Crossing the Median
“The median is the number that separates ordered data into halves,” Dr. Williams said. “Half the values are the same size or smaller than the median; half the values are the same size or larger than the median.”
The median is different from the average, or mean. The mean adds up all the values and divides them evenly among the set. The median, on the other hand, is simply the number in the middle among a list of numbers. For example, if you have 11 values in a set and list them in ascending order, like the body weight of 11 people from lightest to heaviest, the median is the sixth number, dividing the two halves.
“The median is generally a better measure of the center when your data has extreme values or outliers,” Dr. Williams said. “For instance, in 2007, the pre-tax family income in the United States calculated as a mean was over $90,000, but the median was a little over $50,000. The median is not affected by extreme values.”
Knowing the tools in the statistician’s toolkit can help make sense of enormous and abstract pools of data.
This article contains material taught by Dr. Talithia Williams from her course Learning Statistics: Concepts and Applications in R. Dr. Williams is an Associate Professor of Mathematics and the Associate Dean for Research and Experiential Learning at Harvey Mudd College. She earned her bachelor’s degree in Mathematics from Spelman College, a master’s degree in mathematics from Howard University and her PhD in Statistics from Rice University.