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Data Analysis Chapter 3
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Gravity
Terms in this set (19)
central tendency
mean, median, mode
mode
the attribute within a data set that occurs most frequenctly, , the ___ is unrestricted; that is, it has the fewest requirements for its use.
It can be used with all four levels of measurement.
If a variable is measured at the nominal level (and sometimes at the ordinal level), the___ is a word, rather than a number.
what does central tendency measure?
provide a mental image of the most central or typical values within a data set.
what happens when data is centrally distributed?
When data are normally distributed, all measures of central tendency fall in the center of the distribution of data.
unimodal
one mode
bimodal
two modes
multimodal
three or more modes
median
divides an array of values into two halves.
To determine the ____, first arrange the data from the lowest value to the highest value.
If the distribution has an odd number of cases, the ____ is the middle number.
If the distribution has an even number of cases, the ____ is the sum of the two middle sores divided by 2.
when to use the median?
If data are measured at the interval or ratio (and sometimes ordinal) level of measurement, the median is often a good choice to describe the central tendency of a distribution of values.
One advantage to reporting the ____ is that it is not affected by the presence of outliers as much as the arithmetic mean
outlier
An extreme value that "lies outside" (is much smaller or larger than) most of the other values in the dataset.
Usually, the presence of an ___ indicates some sort of problem in the dataset.
mean
When a variable within a dataset is measured at the interval or ratio level of measurement, the ____ can be used to represent or describe that variable.
The ____ is the most reported measure of central tendency. Generally speaking, it is the average of the scores in a distribution.
The main disadvantage of the mean, unlike the median or mode, is that it is sensitive to outlier scores the arithmetic mean, in particular.
arithmetic mean
what is generally meant by the term mean, cannot be computed with nominal level variables, The most common type of mean
The sum of all attributes in a distribution divided by the total number of attributes "the average."
trimmed mean
designed to minimize the effects of a few extreme outliers, combines the best features of both the arithmetic mean and the median, Designed to minimize the effects of extreme outliers.
A small percentage (i.e., 10%) of the attributes in an array are thrown out. Then, the remaining 90% of the attributes are averaged. This average is the "trimmed mean."
weighted average
The weighted mean is similar to the arithmetic mean, except that instead of each of the attributes contributing equally to the final average, some of the attributes hold more "weight" (or are more important) than others.
range
The range is the simplest measure of variability
It is the distance that encompasses all attributes within a dataset
The range is computed as follows: maximum score-minimum score +1
We add 1 to the difference so that the range reflects the total number of attributes of the variable that it encompasses.
interquartile range
insteadof using a maximum and minimum attributes to obtain a range, a data set's variability can be reported as the rang of attributes in an array that can fall between the 75th and 25th percentiles- the range for the middle 50 percent of cases
semi-interquartile range
the interquartile range divided by 2
mean deviation
This measure of variability describes the dispersion of scores around the mean.
It is the average (mean) deviations (distances) of scores around the mean, symbolized as MD.
Step 1: compute the mean
Step 2: compute the deviation of each score in the distribution from the mean by subtracting the mean from each score (x= score and x-bar= mean)
Step 3: Find the mean of those deviations
sum the absolute values of the deviations
divide the sum of the deviations by the total number of cases.
mean deviation=
sum of deviation values (ignoring sign)/ number of cases
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Verified questions
STATISTICS
In North America, phone numbers have the form XXX-XXX-XXXX. The first three digits give the area code, and the second three digits indicate the exchange. (a) Nick lives in western North Carolina, where the area code is 828. If there were no restrictions on the remaining seven digits, how many phone numbers would be possible in the 828 area code? Show your method. (b) In fact, exchanges cannot begin with 0 or 1. How many possible numbers are there in the 828 area code, subject to this restriction? Show your method. (c) How many of the possible phone numbers in (b) include at least one 9? Show your work.
STATISTICS
A coin is tossed 25 times. Estimate the chance of getting 12 heads and 13 tails.
PROBABILITY
Find the value of a retirement savings account paying an APR of 5.4% after 40 years (contributions made at the end of each year, including the last year) when the annual contribution is (a) $1200, (b)$600, (c) $1800
PROBABILITY
A criminologist conducted a survey to determine whether the incidence of certain types of crime varied from one part of a large city to another. The particular crimes of interest were assault, burglary, larceny, and homicide. The following table shows the numbers of crimes committed in four areas of the city during the past year. $$ \begin{matrix} & \text{Type of Crime}\\ \text{District} & \text{ Assault } & \text{Burglary} & \text{Larceny} & \text{Homicide}\\ \text{1} & \text{162} & \text{118} & \text{451} & \text{18}\\ \text{2} & \text{310} & \text{196} & \text{996} & \text{25}\\ \text{3} & \text{258} & \text{193} & \text{458} & \text{10}\\ \text{4} & \text{280} & \text{175} & \text{390} & \text{19}\\ \end{matrix} $$ Can we conclude from these data at the 0.01 level of signiﬁcance that the occurrence of these types of crime is dependent on the city district?
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