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Chapter 12: Problem 2

Find the mean for each group of data items. \(11,6,4,0,2,1,12,0,0\)

Short Answer

Expert verified
The mean of the given data set is 4.

Step by step solution

01

Add all numbers in the set

The first step is to simply add all of the numbers together. In this case, add: \(11 + 6 + 4 + 0 + 2 + 1 + 12 + 0 + 0\)
02

Calculate the sum

The total sum of these numbers is \(36\)
03

Count the total number of items

In this case, there are 9 items in the data set.
04

Divide the sum by the count of numbers

To complete the mean calculation, divide the sum of \(36\) by the total number of items, which is 9. So we calculate \(36 / 9\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Arithmetic Mean
The arithmetic mean is a way of finding the average of a set of numbers. When we talk about the "mean," we're usually referring to the arithmetic mean. It's a central value of a data set and often represents the "typical" value among the numbers. To find this mean, you simply need to follow a few steps which involve adding all the numbers and dividing the result by the number of values you have. This calculation helps in providing a single representative figure for a group of numbers, helping us understand the general trend or central tendency of that data set.
What is a Data Set?
A data set is simply a collection of numbers or values that you want to analyze or learn something about. In statistics, each number in a data set is called a "datum." For example, if you have the numbers 11, 6, 4, 0, 2, 1, 12, 0, and 0, these form your data set. This is what you will use to calculate the mean. The data set can be any size鈥攁 few numbers or hundreds. The main idea is that it's a group of numbers taken together to perform some statistical analysis on them.
How to Calculate the Sum of Numbers
Calculating the sum of numbers is the first step in finding the arithmetic mean. You add together all the numbers in your data set. In math, the symbol for this addition is the Greek letter sigma \(\Sigma\), which means "sum."
  • Take each number in your data set.
  • Add them together one by one.
For instance, if your data set is 11, 6, 4, 0, 2, 1, 12, 0, and 0, you will calculate 11 + 6 + 4 + 0 + 2 + 1 + 12 + 0 + 0, which equals 36. This sum is an essential part of finding the mean.
Divide by Count to Get the Mean
Once you have the sum of all numbers, the next step is to count how many numbers are in the data set. This count, or total number of data points, is crucial as you'll use it to divide the sum. For instance, in our example, there are 9 numbers in the data set. Using these two pieces of information:
  • The sum (36)
  • The count (9)
You divide the sum by the count: \(36 \div 9\), which gives you 4. This result is the arithmetic mean, providing a single value that represents all numbers in your data set efficiently.

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