mean, median and mode
Answers
Answer:
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. ... If no number in the list is repeated, then there is no mode for the list.
Step-by-step explanation:
Mean, median, and mode
Mean, median, and mode are different measures of center in a numerical data set. They each try to summarize a dataset with a single number to represent a "typical" data point from the dataset.
Mean: The "average" number; found by adding all data points and dividing by the number of data points.
Example: The mean of 444, 111, and 777 is (4+1+7)/3 = 12/3 = 4(4+1+7)/3=12/3=4left parenthesis, 4, plus, 1, plus, 7, right parenthesis, slash, 3, equals, 12, slash, 3, equals, 4.
Median: The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).
Example: The median of 444, 111, and 777 is 444 because when the numbers are put in order (1(1left parenthesis, 1, 444, 7)7)7, right parenthesis, the number 444 is in the middle.
Mode: The most frequent number—that is, the number that occurs the highest number of times.
Example: The mode of \{4{4left brace, 4, 222, 444, 333, 222, 2\}2}2, right brace is 222 because it occurs three times, which is more than any other number.
Want to learn more about mean, median, and mode? Check out the more in-depth examples below, or check out this video explanation.
Calculating the mean
There are many different types of mean, but usually when people say mean, they are talking about the arithmetic mean.
The arithmetic mean is the sum of all of the data points divided by the number of data points.
mean=sum of data# of data points
Here's the same formula written more formally:
\text{mean}=\dfrac{\sum{x_i}}{n}mean=
n
∑x
i
start text, m, e, a, n, end text, equals, start fraction, sum, x, start subscript, i, end subscript, divided by, n, end fraction
Example
Find the mean of this data:
111, 222, 444, 555
Start by adding the data:
1+2+4+5=121+2+4+5=121, plus, 2, plus, 4, plus, 5, equals, 12
There are 444 data points.
\text{mean}=\dfrac{12}{4}=3mean=
4
12
=3start text, m, e, a, n, end text, equals, start fraction, 12, divided by, 4, end fraction, equals, 3
The mean is 333.
Practice problems
PROBLEM A
What is the arithmetic mean of the following numbers?
10, 6, 4, 4, 6, 4, 110,6,4,4,6,4,110, comma, 6, comma, 4, comma, 4, comma, 6, comma, 4, comma, 1
mean =
Explain
Want to practice more of these? Check out this exercise on calculating the mean.
Finding the median
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
To find the median:
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Example 1
Find the median of this data:
111, 444, 222, 555, 000
Put the data in order first:
000, 111, 222, 444, 555
There is an odd number of data points, so the median is the middle data point.
000, 111, \large222, 444, 555
The median is 222.