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Which type of graph is best for revealing measures of spread and central tendency of a data set?
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Which measures of central tendency become larger as the data is more dispersed?
None. Measures of central tendency are not significantly affected by the spread or dispersion of data.
Which is the most accurate of mode mean median and range?
Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.
3 Give a brief note of the measures of central tendency together with their merits and Demerits Which is the best measure of central tendency and why?
ANS: Measures of central tendency will quantify the middle of the distribution. The measures in case of population are the parameters and in case of sample, the measures are statistics that are estimates of population parameters. The three most common ways of measuring the centre of distribution is the mean, mode and median.In case of population, the measures of dispersion are used to quantify the spread of the distribution. Range, interquartile range, mean absolute deviation and standard deviation are four measures to calculate the dispersion.The measures of central tendency and measures of dispersion summarise mass data in terms of its two important features.i. With respect to nature of data to cluster around a central valueii. With respect to their spread from their central valueArithmetic mean is defined as the sum of all values divided by number of values.Median of a set of values is the middle most value when the values are arranged in the ascending order of magnitude.Mode is the value which has the highest frequencyThe measures of variations are:i. Range (R)ii. Quartile Deviations ( Q.D)iii. Mean Deviations (M.D)iv. Standard Deviations (S.D)Coefficient of variation is a relative measure expressed in percentage and is defined as:CV in %=
What is mean and standard deviation?
They are statistical measures. For a set of observations of some random variable the mean is a measure of central tendency: a kind of measure which tells you around what value the observations are. The standard deviation is a measure of the spread around the mean.
Can a data set have the same range and median?
Yes, but the two are measures of very different things. The median is a measure of central tendency whereas the range is a measure of spread. Nevertheless, the set 1, 2, 3, 4, 4 has a range of 3 and a median of 3.
Which measures of central tendency become larger as the data is more dispersed?
None. Measures of central tendency are not significantly affected by the spread or dispersion of data.
Why measures of dispersion are important along with measures of central tendency to understand the nature of the data?
Central tendency will only give you information on the location of the data. You also need dispersion to define the spread of the data. In addition, shape should also be part of the defining criteria of data. So, you need: location, spread & shape as best measures to define data.
Which is the most accurate of mode mean median and range?
Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.Accuracy depends on what you are trying to measure.As a measure of central tendency, the range is totally useless because it is not a measure of central tendency. As a measure of spread (dispersion), it is the most accurate because it is the only one that measures spread: the other threee are totally useless.With nominal data, the median and mean are not defined and so cannot be accurate.And so on.
How do we obtain useful information from a set of data?
You calculate summary statistics: measures of the central tendency and dispersion (spread). The precise statistics would depend on the nature of the data set.
3 Give a brief note of the measures of central tendency together with their merits and Demerits Which is the best measure of central tendency and why?
ANS: Measures of central tendency will quantify the middle of the distribution. The measures in case of population are the parameters and in case of sample, the measures are statistics that are estimates of population parameters. The three most common ways of measuring the centre of distribution is the mean, mode and median.In case of population, the measures of dispersion are used to quantify the spread of the distribution. Range, interquartile range, mean absolute deviation and standard deviation are four measures to calculate the dispersion.The measures of central tendency and measures of dispersion summarise mass data in terms of its two important features.i. With respect to nature of data to cluster around a central valueii. With respect to their spread from their central valueArithmetic mean is defined as the sum of all values divided by number of values.Median of a set of values is the middle most value when the values are arranged in the ascending order of magnitude.Mode is the value which has the highest frequencyThe measures of variations are:i. Range (R)ii. Quartile Deviations ( Q.D)iii. Mean Deviations (M.D)iv. Standard Deviations (S.D)Coefficient of variation is a relative measure expressed in percentage and is defined as:CV in %=
What is the difference between range and spread in mathematics?
In Statistics, the measure of spread tells us how much adata sample is spread out or scattered. We can use the range and the interquartile range (IQR) to measure the spread of a sample. Measures of spread together with measures of location (or central tendency) are important for identifying key features of a sample to better understand the population from which the sample comes from. The range is the difference between a high number and the low number in the samples presented. It represents how spread out or scattered a set of data. It is also known as measures of dispersion or measures of spread.
What is mean and standard deviation?
They are statistical measures. For a set of observations of some random variable the mean is a measure of central tendency: a kind of measure which tells you around what value the observations are. The standard deviation is a measure of the spread around the mean.
What is a number that helps describe all of the data in a data set?
There is no single number. There are several different measures of central tendency - different ones are better in different circumstances. Then there are several measures of spread or dispersion, skewness and so on. All of these are characteristics of the data and they cannot all be summarised by a single number.
In mathematics central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data Explain.?
The measure of variability tells you how close to the central value the data values lie: that is whether the cluster is tightly packed around the central value of spread out over a large range of values.
Can a data set have the same range and median?
Yes, but the two are measures of very different things. The median is a measure of central tendency whereas the range is a measure of spread. Nevertheless, the set 1, 2, 3, 4, 4 has a range of 3 and a median of 3.
How does a box plot help when displaying a distribution of data?
A box plot summarises 5 key indicators of a distribution: the median, minimum, maximum and the lower and upper quartiles. The first of these is a measure of the central tendency whereas the others, in pairs, give measures of the spread as well as skewness.
Does energy have the tendency to spread out?
yes
