8. find the mode and median
of the observations. 5,3,2,5,3,5,7,3,5,7,5,83,6,3,7,8,7,9
Answers
Step-by-step explanation:
Median
The value in a set which is most close to the middle of a range.
Mode
The value which occures most frequently in a data set.
How to Find the Median
In ascending order the numbers are 3, 3, 4, 7, 8, 9, 11, 15, 19, 27. There are 10 total numbers, so the 5th and 6th numbers are used to figure the median. (8+9)/2 = 8.5
If there were 9 numbers in the series rather than 10 you would take the 5th number and would not need to average the 2 middle numbers. The 2 middle numbers only need to be averaged when the data set has an even number of data points in it.
How to Find the Mode
The only number which appears multiple times is 3, so it is the mode.
Average Calculator.
Calculate Average and Range
Enter Your Numbers to Right
With a Comma Between Each
E.g: 3, 19, 9, 7, 27, 4, 8, 15, 3, 11
5,3,2,5,3,5,7,3,5,7,5,83,6,3,7,8,7,9
Total Numbers in Set:
18
Mean (Average):
9.61111
Median (Middle):
(5+5)/2 = 5
Mode (Most Common):
5
Range (Biggest - Smallest):
81
Ascending Order:
2,3,3,3,3,5,5,5,5,5,6,7,7,7,7,8,9,83
Decending Order:
83,9,8,7,7,7,7,6,5,5,5,5,5,3,3,3,3,2
Even Numbers:
2,6,8
Odd Numbers:
3,3,3,3,5,5,5,5,5,7,7,7,7,9,83
Math Definition
Mean
The average of all the data in a set.
Median
The value in a set which is most close to the middle of a range.
Mode
The value which occures most frequently in a data set.
Range
The difference between the largest and smallest data in a data set.
Example Calculation
Calculate the mean, median, mode and range for 3, 19, 9, 7, 27, 4, 8, 15, 3, 11.
How to Find the Mean (or Average Value)
To figure the mean, add up the numbers, 3+3+4+7+8+9+11+15+19+27=106 then divide it by the number of data points 106/10=10.6.
How to Find the Median
In ascending order the numbers are 3, 3, 4, 7, 8, 9, 11, 15, 19, 27. There are 10 total numbers, so the 5th and 6th numbers are used to figure the median. (8+9)/2 = 8.5
If there were 9 numbers in the series rather than 10 you would take the 5th number and would not need to average the 2 middle numbers. The 2 middle numbers only need to be averaged when the data set has an even number of data points in it.
How to Find the Mode
The only number which appears multiple times is 3, so it is the mode.
How to Find the Range
To figure the range subtract the smallest number from the largest number 27-3=24.
Mean, Median and Mode: Data Trends, Detecting Anomalies, and Uses in Sports
- Guide Authored by Corin B. Arenas, published on October 17, 2019
In school, we ask the average score for a test to know if we have a good grade. When it comes to buying expensive products, we often ask the average price to look for the best deals.
These are just a few examples of how averages are used in real life.
In this section, you’ll learn about the different types of averages and how they’re calculated and applied in various fields, especially in sports.
What Does the Term ‘Average’ Mean?
Women with different heights
When people describe the ‘average’ of a group of numbers, they often refer to the arithmetic mean. This is one out of 3 different types of average, which include median and mode.
Types of Average Description
Mean The average of numbers in a group.
Median The middle number in a set of numbers.
Mode The number that appears most often in a set of numbers.
In conversational terms, most people just say ‘average’ when they’re really referring to the mean. Arithmetic mean and average are synonymous words which are used interchangeably, according to Dictionary.com.
It’s calculated by adding the numbers in a set and dividing it by the total number in the set—which is what most people do when they’re finding the average. See the example below.
Mean
Set: 8, 12, 9, 7, 13, 10
Mean = (8 + 12 + 9 + 7 + 13 + 10) / 6
= 59 / 6
= 9.83
The average or arithmetic mean in this example is 9.83.
Median
The median, on the other hand, is another type of average that represents the middle number in an ordered sequence of numbers. This works by ordering a sequence of numbers (in ascending order) then determining the number which occurs at the middle of the set. See the example below.