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What is the proportion of the total area under the normal curve within plus and minus two standard deviations of the mean?
95
What percent of a normal population is within 2 standard deviations of the mean?
In a normal distribution, approximately 95% of the population falls within 2 standard deviations of the mean. This is known as the 95% rule or the empirical rule. The empirical rule states that within one standard deviation of the mean, about 68% of the population falls, and within two standard deviations, about 95% of the population falls.
What determines the standard deviation to be high?
Standard deviation is a measure of the scatter or dispersion of the data. Two sets of data can have the same mean, but different standard deviations. The dataset with the higher standard deviation will generally have values that are more scattered. We generally look at the standard deviation in relation to the mean. If the standard deviation is much smaller than the mean, we may consider that the data has low dipersion. If the standard deviation is much higher than the mean, it may indicate the dataset has high dispersion A second cause is an outlier, a value that is very different from the data. Sometimes it is a mistake. I will give you an example. Suppose I am measuring people's height, and I record all data in meters, except on height which I record in millimeters- 1000 times higher. This may cause an erroneous mean and standard deviation to be calculated.
What is the formula to determine the standard deviation of the resulting normal distribution when adding two normal distributions with different means and standard deviations?
s= bracket n over sigma i (xi-x-)^2 all over n-1 closed bracket ^ 1/2
How would you write two billion in standard form?
Two billion in standard form is 2.0 × 109
What Percent of population between 1 standard deviation below the mean and 2 standard deviations above mean?
In a normal distribution, approximately 68% of the population falls within one standard deviation of the mean, and about 95% falls within two standard deviations. Therefore, to find the percentage of the population between one standard deviation below the mean and two standard deviations above the mean, you would calculate 95% (within two standard deviations) minus 34% (the portion below one standard deviation), resulting in approximately 61% of the population.
How do you find two standard deviations above a mean?
It is mean + 2*standard deviation.
What does normality mean in health and social care?
All minor deviations occurring with two standard deviations under the Gaussian curve are considered normal. Deviations occurring outside of two standard deviations are considered abnormal.
How many of the 100 scores are expected to be below 32.38 (two standard deviations above the mean)?
In a normal distribution, approximately 95% of the scores fall within two standard deviations of the mean. This means that about 5% of the scores will be below two standard deviations above the mean. Therefore, if you have 100 scores, you can expect around 5 scores to be below 32.38.
When a data set is normally distributed about how much of the data fall within two standard deviations of the mean?
In a normally distributed data set, approximately 95% of the data falls within two standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data falls within one standard deviation and about 99.7% falls within three standard deviations. Therefore, two standard deviations capture a significant majority of the data points.
What percentage of scores falls between the mean and -2 to 2 standard deviations under the normal curve?
In a normal distribution, approximately 68% of scores fall within one standard deviation of the mean (between -1 and +1 standard deviations). About 95% of scores fall within two standard deviations (between -2 and +2 standard deviations). Therefore, the percentage of scores that falls specifically between the mean and -2 to 2 standard deviations is about 95% minus the 50% that is below the mean, resulting in approximately 45%.
I have two data sets with the same number of values with means x1 and x2 and standard deviations of n1 and n2. How do you average means with standard deviations?
You can't average means with standard deviations. What are you trying to do with the two sets of data?
In a standard normal distribution 95 of the data is within plus - standard deviations of the mean.?
In a standard normal distribution, approximately 95% of the data falls within two standard deviations (±2σ) of the mean (μ). This means that if you take the mean and add or subtract two times the standard deviation, you capture the vast majority of the data points. This property is a key aspect of the empirical rule, which describes how data is spread in a normal distribution.
What is the proportion of the total area under the normal curve within plus and minus two standard deviations of the mean?
95
True or false two normal distributions that have the same mean are centered at the same place regardless of the relationship between their standard deviation?
True. Two normal distributions that have the same mean are centered at the same point on the horizontal axis, regardless of their standard deviations. The standard deviation affects the spread or width of the distributions, but it does not change their center location. Therefore, even with different standard deviations, the distributions will overlap at the mean.
Statistic question help?
When using Chebyshev's Theorem the minimum percentage of sample observations that will fall within two standard deviations of the mean will be __________ the percentage within two standard deviations if a normal distribution is assumed Empirical Rule smaller than greater than the same as
What is the measures that fall beyond three standard deviations of the mean called?
You may be referring to the statistical term 'outlier(s)'. Also, there is a rule in statistics called the '68-95-99 Rule'. It states that in a normally distributed dataset approximately 68% of the observations will be within plus/minus one standard deviation of the mean, 95% within plus/minus two standard deviations, and 99% within plus/minus three standard deviations. So if your data follow the classic bell-shaped curve, roughly 1% of the measures should fall beyond three standard deviations of the mean.
