Measures of the middle
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The document discusses three common measures used to find the middle of a data set: the mode, median, and mean. The mode is the most frequently occurring value, the median is the middle value when data is ordered, and if there is an even number of data points we take the average of the two middle values. The mean is calculated by adding all the numbers and dividing by the sample size.
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ANALYSIS AND
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Slide 1 Transcript
In a qualitative design, the information gathered and studied often is nominal or narrative in form. Finding trends, patterns, and relationships is discovered inductively and upon
reflection. Some describe this as an intuitive process. In Module 4, qualitative research designs were explained along with the process of how information gained shape the inquiry as it
progresses. For the most part, qualitative designs do not use numerical data, unless a mixed approach is adopted. So, in this module the focus is on how numerical data collected in either
a qualitative mixed design or a quantitative research design are evaluated. In quantitative studies, typically there is a hypothesis or particular research question. Measures used to assess
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interest will be the focus for this module.
Data and Statistics
Match the data with an
appropriate statistic
Approaches based on data
characteristics
Collected for single or multiple
groups
Involve continuous or discrete
variables
Data are nominal, ordinal,
interval, or ratio
Normal or non-normal distribution
Statistics serve two
functions
Descriptive: Describe what
data look like
Inferential: Use samples
to estimate population
characteristics
Slide 3 Transcript
There are, of course, far too many statistical concepts to consider than time allows for us here. So, we will limit ourselves to just a few basic ones and a brief overview of the more
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4. Do the data represent a normal or non-normal distribution.
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The other is known as inferential statistics which typically uses a small sample to estimate characteristics of the larger population. Let’s begin with descriptive statistics and the measures
of central tendency.
Descriptive Statistics and Central Measures
Descriptive statistics
organize and present data
Mode
The number occurring most
frequently; nominal data
Quickest or rough estimate
Most typical value
Measures of central
tendenc.
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Definition
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hh.pptx
This document discusses measures of central tendency including the mean, median, and mode. It provides examples of calculating each measure using data sets. The mean is the average value calculated by summing all values and dividing by the number of data points. The median is the middle value of an ordered data set. The mode is the value that occurs most frequently in a data set. Examples are given to demonstrate calculating the mean, median, and mode from sample data on driving speeds, test scores, and number of homework problems assigned.
Chapter 3 Numerical Descriptions of Data 75 Chapter 3.docx
Chapter 3: Numerical Descriptions of Data
75
Chapter 3: Numerical Descriptions of Data
Chapter 1 discussed what a population, sample, parameter, and statistic are, and how to
take different types of samples. Chapter 2 discussed ways to graphically display data.
There was also a discussion of important characteristics: center, variations, distribution,
outliers, and changing characteristics of the data over time. Distributions and outliers can
be answered using graphical means. Finding the center and variation can be done using
numerical methods that will be discussed in this chapter. Both graphical and numerical
methods are part of a branch of statistics known as descriptive statistics. Later
descriptive statistics will be used to make decisions and/or estimate population
parameters using methods that are part of the branch called inferential statistics.
Section 3.1: Measures of Center
This section focuses on measures of central tendency. Many times you are asking what
to expect on average. Such as when you pick a major, you would probably ask how
much you expect to earn in that field. If you are thinking of relocating to a new town,
you might ask how much you can expect to pay for housing. If you are planting
vegetables in the spring, you might want to know how long it will be until you can
harvest. These questions, and many more, can be answered by knowing the center of the
data set. There are three measures of the “center” of the data. They are the mode,
median, and mean. Any of the values can be referred to as the “average.”
The mode is the data value that occurs the most frequently in the data. To find it, you
count how often each data value occurs, and then determine which data value occurs
most often.
The median is the data value in the middle of a sorted list of data. To find it, you put the
data in order, and then determine which data value is in the middle of the data set.
The mean is the arithmetic average of the numbers. This is the center that most people
call the average, though all three – mean, median, and mode – really are averages.
There are no symbols for the mode and the median, but the mean is used a great deal, and
statisticians gave it a symbol. There are actually two symbols, one for the population
parameter and one for the sample statistic. In most cases you cannot find the population
parameter, so you use the sample statistic to estimate the population parameter.
Population Mean:
µ = Σx
N
, pronounced mu
N is the size of the population.
x represents a data value.
x∑ means to add up all of the data values.
Chapter 3: Numerical Descriptions of Data
76
Sample Mean:
x = Σx
n
, pronounced x bar.
n is the size of the sample.
x represents a data value.
x∑ means to add up all of the data values.
The value for x is used to estimate µ since µ can’t be calculated in most situations.
Example #3.1.1: Finding the.
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Measures of the middle
- 1. Measures of the Middle Often when working with data we want to find the middle of the data set. In basic statistics there are three commonly used measures of the middle.
- 2. Mode If there is a most frequently occurring value for a set of data, then that value is called the mode. The mode could be a most frequently occurring word, a category, or number.
- 3. Median The median is usually used with numeric data, or data that can be placed in some form of rank order. The median is the middle value in an ordered set of data. If the data is numeric and the number of data points is even, then we "split the difference" between the two middle data points.
- 4. Mean The arithmetic mean is the mathematical middle of a set of numeric data. To calculate the mean, add the numbers and divide by the number of numbers (the sample size)