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What Percent of data is below the mean in a normal distribution?
In the normal distribution, the mean and median coincide, and 50% of the data are below the mean.
50 percent scores falling below median?
Yes. That is how the median is defined.
What are the advantages of using median?
When someone asks a for an "average" value, that can mean a couple of different things. "Mean," "median," and "mode" are all values that are used to relate what the "center" or "average" of a distribution of values is. Each one has their advantages and disadvantages. The median is the value that divides the distribution exactly into halves - 50% is below it, and 50% above it. The median may not actually occur in the distribution, but it is the "balance point" of the distribution. The main advantage of the median is that it is not affected by outliers as the mean is and the mode can be. In distributions with a clear skew, such as housing prices or wages, using the median provides a much better estimate of what the "average" is.
Which descriptive statistic always divides the data set such that 50 percent of the data values lie above it and 50 percent lie below it?
The median.
The standard z-score such that 80 percent of the distribution is below to the left of this value is?
z = 0.8416
What Percent of data is below the mean in a normal distribution?
In the normal distribution, the mean and median coincide, and 50% of the data are below the mean.
What percent falls below the mean for normal distribution?
In a normal distribution half (50%) of the distribution falls below (to the left of) the mean.
50 percent scores falling below median?
Yes. That is how the median is defined.
What is the interpretation if the results in mean and median are the same?
The data would be approximately evenly distributed about and below the mean. This suggests a normal distribution, although there are other criteria involved in that.
What is the relationship amount the mean median and mode in a symmetric disribution?
In a symmetric distribution, the mean, median, and mode are all equal or located at the same central point. This characteristic ensures that the distribution is balanced on either side, with half of the data points falling below the central value and half above it. Therefore, in a perfectly symmetric distribution, such as a normal distribution, these three measures of central tendency coincide.
What is the nature of symmetry if median is greater than the mean?
Generally, when the median is greater than the mean it is because the distribution is skewed to the left. This results in outliers or values further below the median than above the median which results in a lower mean value than median value. When a distribution is skewed left, it is generally not very symmetrical or normally distributed.
What are the uses of median?
When someone asks a for an "average" value, that can mean a couple of different things. "Mean," "median," and "mode" are all values that are used to relate what the "center" or "average" of a distribution of values is. Each one has their advantages and disadvantages. The median is the value that divides the distribution exactly into halves - 50% is below it, and 50% above it. The median may not actually occur in the distribution, but it is the "balance point" of the distribution. The main advantage of the median is that it is not affected by outliers as the mean is and the mode can be. In distributions with a clear skew, such as housing prices or wages, using the median provides a much better estimate of what the "average" is.
What are the advantages of using median?
When someone asks a for an "average" value, that can mean a couple of different things. "Mean," "median," and "mode" are all values that are used to relate what the "center" or "average" of a distribution of values is. Each one has their advantages and disadvantages. The median is the value that divides the distribution exactly into halves - 50% is below it, and 50% above it. The median may not actually occur in the distribution, but it is the "balance point" of the distribution. The main advantage of the median is that it is not affected by outliers as the mean is and the mode can be. In distributions with a clear skew, such as housing prices or wages, using the median provides a much better estimate of what the "average" is.
Which descriptive statistic always divides the data set such that 50 percent of the data values lie above it and 50 percent lie below it?
The median.
What percent of data falls between 1 Standard deviation below and 2 stand deviations above the mean?
The answer will depend on what the distribution is. Non-statisticians often assum that the variable that they are interested in follows the Standard Normal distribution. This assumption must be justified. If that is the case then the answer is 81.9%
The standard z-score such that 80 percent of the distribution is below to the left of this value is?
z = 0.8416
PLOT A VARIABLE WITH NORMAL DISTRIBUTION WITH MEAN 200 AND DEVIATION 20. SUPERIMPOSED WITH THE PREVIOUS FIGURE, PLOT THE DISTRIBUTION OF THE ARITHMETIC MEAN OF SAMPLES OF SIZE N=4, 25 AND 100, OF THAT POPULATION?
A normal distribution with a mean of 200 and a deviation of 20 can be plotted as a bell-shaped curve, as shown in the figure below. Superimposed on the figure, the distribution of the arithmetic mean of samples of size n=4, 25 and 100 can be plotted as shown in the figure below. The arithmetic mean distribution for n=4 is a much narrower distribution than a normal distribution, since it is based on a small sample size. As the sample size increases, the distribution becomes wider and more similar to the normal distribution.
