Understanding Statistic Fundamentals: Mean and Median
Look into the concept of basic statistics and test your knowledge with this real SAT question
This email is written by Program Officer Jasmine Ngo.
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Tigerway Team Members, Parents, and Prospective Families,
In this email we will be reviewing two fundamental concepts in statistics: mean and median. Specifically, we will explore how adding numbers to a list can affect these measures of averages.
The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of values.
The median is the middle value in a set of numbers, with half the values above it and half below it.
When adding a number to a list, the mean will always FOLLOW THE TAIL and the median will continue to stay as the MIDDLE number.
Let's review a real-life SAT question that tests your ability on calculating mean and median.
Make sure to try this question out first before reading my commentary
March 2022 SAT:
We are given a list of numbers resembling the height of 6 children. We want to add another child’s height, 60 inches to the list. The question asks us what will happen to the mean and median when we add 60 to the list.
First, let’s calculate the original mean and median.
Mean: 52 + 53 + 54 + 54 + 55 + 56 = 324 / 6 = 54
Median: The middle numbers in the ordered list are 54 and 54. When given two numbers in the middle, we find the mean of the two. 54 + 54 = 108/2 = 54
Now let’s add 60 to the list of numbers.
Mean: 52 + 53 + 54 + 54 + 55 + 56 + 60 = 384 / 7 = 54.86
Median: The middle number is shifted up to 54, the middle number of the 7 numbers in the list.
The mean increased and the median stayed the same.
Answer: C
Quick method without manual calculation:
Since 60 is the largest number on the list, adding it would push the mean toward the higher end of the tail. However, the median would shift up by only one, remaining at 54 inches, because it is merely the middle value in the ordered list.
This question demonstrates how adding numbers to a list can affect the mean and median. As larger numbers are added, the mean tends to shift toward larger values (vice versa when smaller numbers are added), while the median may shift depending on the new values.
Understanding the concepts of mean and median and how they can be affected by adding numbers to a list is essential for anyone working with numerical data. Keep this fundamental concept in mind as we progress toward advanced statistics in the future!
Further resources:
Jack Delehey’s College Confidence Group is a forum-based community where Jack and I answer general questions for parents with college-bound teens.
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