| Numerical Measure Sensitive Measure Resistant Measure | Measure of Center Mean Median | Measure of Spread ( Variation ) Standard Deviation (SD) Interquartile Range (IQR) |
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Is deviation a measure of center or a measure of variation?
The standard deviation is a number that measures how far data values are from their mean. The standard deviation provides a
numerical measure of the overall amount of variation
in a data set, and can be used to determine whether a particular data value is close to or far from the mean.
Is standard deviation a measure of center?
The standard deviation is
a measure of spread
. We use it as a measure of spread when we use the mean as a measure of center.
Is standard deviation a measure of center yes or no?
d. The range, the IQR, and the standard deviation are
all measures of the center of a distribution
.
Is standard deviation a measure of variation?
The standard deviation is
the square root of the variance
, and it is a useful measure of variability when the distribution is normal or approximately normal (see below on the normality of distributions).
Which of the following is a measure of variation?
The range is the measure of variability or dispersion. The range is a poor measure because it is based on the extreme observations of a data set. The standard deviation is considered as the best measure of the variability.
Why standard deviation is considered the best measure of variation?
The standard deviation is an especially useful measure of variability when
the distribution is normal or approximately normal
(see Chapter on Normal Distributions) because the proportion of the distribution within a given number of standard deviations from the mean can be calculated.
What is standard deviation a measure of?
The standard deviation measures
the dispersion or variation of the values of a variable around its mean value (arithmetic mean)
. Put simply, the standard deviation is the average distance from the mean value of all values in a set of data.
How does mean affect standard deviation?
If every term is doubled, the distance between each term and the mean doubles, BUT also the distance between each term doubles and thus standard deviation increases. If
each term is divided by two
, the SD decreases. (b) Adding a number to the set such that the number is very close to the mean generally reduces the SD.
How do you interpret a standard deviation?
Low standard deviation means data are clustered around the
mean
, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.
How do you determine the best measure of variation?
- Range: the difference between the highest and lowest values.
- Interquartile range: the range of the middle half of a distribution.
- Standard deviation: average distance from the mean.
- Variance: average of squared distances from the mean.
What is the best measure of variation?
The interquartile range
is the best measure of variability for skewed distributions or data sets with outliers.
What is the measure of center and variation?
The mean and median
are the two most common measures of center. The mean is often called the average. A measure of variability is a single number used to describe the spread of a data set. Use the interactive below to visualize how a change in center or a change in spread will affect a distribution.
Why standard deviation is not a measure of central tendency?
Deviation means change or distance. But change is always followed by the word ‘from’. Hence standard deviation is a measure of change or the distance from a measure of central tendency – which is normally the mean. Hence, standard deviation is
different
from a measure of central tendency.
Which measure of dispersion is square of standard deviation?
The square of the standard deviation is
the variance
. It is also a measure of dispersion.
Which measure of dispersion is standard deviation?
Standard deviation (
SD
) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. SD is the square root of sum of squared deviation from the mean divided by the number of observations.
