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Can a standard deviation of a sample be equal to a standard deviation of a population?
Yes
Is it true or false that the standard deviation of a set is always smaller than the variance of that set?
False. The standard deviation of a set is the square root of the variance, so it is not always smaller; in fact, it is always less than or equal to the variance when the variance is positive. The standard deviation can be equal to the variance only when the variance is 1 (since the square root of 1 is 1).
Is the standard deviation of standard normal distribution alway equal to 1?
Yes, the standard deviation of a standard normal distribution is always equal to 1. The standard normal distribution is a specific normal distribution with a mean of 0 and a standard deviation of 1, which allows it to serve as a reference for other normal distributions. This property is essential for standardizing scores and facilitating comparisons across different datasets.
Can standard deviation equal zero?
Standard deviation can only be zero if all the data points in your set are equal. If all data points are equal, there is no deviation. For example, if all the participants in a survey coincidentally were all 30 years old, then the value of age would be 30 with no deviation. Thus, there would also be no standard deviation.A data set of one point (small sample) will always have a standard deviation of zero, because the one value doesn't deviate from itself at all.!
Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
What are all the values a standard deviation can take?
The standard deviation must be greater than or equal to zero.
Is mean deviation less than standard deviation?
Yes, the mean deviation is typically less than or equal to the standard deviation for a given dataset. The mean deviation measures the average absolute deviations from the mean, while the standard deviation takes into account the squared deviations, which can amplify the effect of outliers. Consequently, the standard deviation is usually greater than or equal to the mean deviation, but they can be equal in certain cases, such as when all data points are identical.
Can a standard deviation of a sample be equal to a standard deviation of a population?
Yes
Is it true or false that the standard deviation of a set is always smaller than the variance of that set?
False. The standard deviation of a set is the square root of the variance, so it is not always smaller; in fact, it is always less than or equal to the variance when the variance is positive. The standard deviation can be equal to the variance only when the variance is 1 (since the square root of 1 is 1).
Why the standard deviation of set of data will always be greater than zero?
The standard deviation is always be equal or higher than zero. If my set of data is limited to whole numbers, all of which are equal, the standard deviation is 0. In all other situations, we first calculate the difference of each number from the average and then calculate the square of the difference. While the difference can be a negative, the square of the difference can not be. The square of the standard deviation has to be positive, since it is the sum of all positive numbers. If we calculate s2 = 4, then s can be -2 or +2. By convention, we take the positive root.
Is the standard deviation of standard normal distribution alway equal to 1?
Yes, the standard deviation of a standard normal distribution is always equal to 1. The standard normal distribution is a specific normal distribution with a mean of 0 and a standard deviation of 1, which allows it to serve as a reference for other normal distributions. This property is essential for standardizing scores and facilitating comparisons across different datasets.
Can standard deviation equal zero?
Standard deviation can only be zero if all the data points in your set are equal. If all data points are equal, there is no deviation. For example, if all the participants in a survey coincidentally were all 30 years old, then the value of age would be 30 with no deviation. Thus, there would also be no standard deviation.A data set of one point (small sample) will always have a standard deviation of zero, because the one value doesn't deviate from itself at all.!
Is it possible for a standard deviation to be negative?
no it is not possible because you have to take the square of error that is (x-X)2. the square of any number is always positive----------Improved answer:It is not possible to have a negative standard deviation because:SD (standard deviation) is equal to the square of V (variance).
Can standard deviation equal standard error?
If n = 1.
If the standard error of a sample of 48 is equal to 14.25 the standard deviation is equal to?
98.73
The square of the standard deviation is equal to?
The variance
Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
