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Is the mean always equal to the median for a normal distribution?
Yes, in a normal distribution, the mean is always equal to the median. This is because the normal distribution is symmetric around its mean, meaning that the values are evenly distributed on both sides. As a result, the central tendency measured by both the mean and the median coincides at the same point.
Will the mean and median in a symmetric distribution always be equal or approximately equal and Why?
In a symmetric distribution, the mean and median will always be equal. This is because symmetry implies that the distribution is balanced around a central point, which is where both the mean (the average) and the median (the middle value) will fall. Therefore, in perfectly symmetric distributions like the normal distribution, the mean, median, and mode coincide at the center. In practice, they may be approximately equal in symmetric distributions that are not perfectly symmetrical due to rounding or sampling variability.
How do you find the median with a Evan set of numbers?
You would answer it like a normal problem if you were doing both even and odd
Why the normal distribution curve have extremes is opened?
Because the domain of the normal distribution is infinite - in both directions.
How does the standard normal distribution differ from the t-distribution?
The normal distribution and the t-distribution are both symmetric bell-shaped continuous probability distribution functions. The t-distribution has heavier tails: the probability of observations further from the mean is greater than for the normal distribution. There are other differences in terms of when it is appropriate to use them. Finally, the standard normal distribution is a special case of a normal distribution such that the mean is 0 and the standard deviation is 1.
Is the mean always equal to the median for a normal distribution?
Yes, in a normal distribution, the mean is always equal to the median. This is because the normal distribution is symmetric around its mean, meaning that the values are evenly distributed on both sides. As a result, the central tendency measured by both the mean and the median coincides at the same point.
How the values of mean and median relate to shape?
The question is how do the mean and median affect the distribution shape. In a normal curve, the mean and median are both in the same point. ( as is the mode) If a distribution is skewed, its tail is either on the right or the left. If a distribution is skewed the median may be a better value to use than the mean since it has less effect on the shape. Also is there are large outliers, the median has less effect and is better to use. So the mean has a bigger effect on the shape many times than the median.
Will the mean and median in a symmetric distribution always be equal or approximately equal and Why?
In a symmetric distribution, the mean and median will always be equal. This is because symmetry implies that the distribution is balanced around a central point, which is where both the mean (the average) and the median (the middle value) will fall. Therefore, in perfectly symmetric distributions like the normal distribution, the mean, median, and mode coincide at the center. In practice, they may be approximately equal in symmetric distributions that are not perfectly symmetrical due to rounding or sampling variability.
When you calculate mean is the answer same when the same data is calculated by median?
No. The mean and median are not necessarily the same. They will be the same if the distribution is symmetric but the converse is not necessarily true. That is to say, a distribution does not have to be symmetric for the mean and median to be the same. For example, the mean and median of {1, 1, 5, 6, 12} are both 5 but the distribution is NOT symmetric.
How do you find the median with a Evan set of numbers?
You would answer it like a normal problem if you were doing both even and odd
Why the normal distribution curve have extremes is opened?
Because the domain of the normal distribution is infinite - in both directions.
A lopsided distribution of scores in which the mean is much larger than both the mode and median is said to be?
skewed.
Why calculate for the mean and median in relation to a sample?
Both the mean and median represent the center of a distribution. Calculating the mean is easier, but may be more affected by outliers or extreme values. The median is more robust.
How does the standard normal distribution differ from the t-distribution?
The normal distribution and the t-distribution are both symmetric bell-shaped continuous probability distribution functions. The t-distribution has heavier tails: the probability of observations further from the mean is greater than for the normal distribution. There are other differences in terms of when it is appropriate to use them. Finally, the standard normal distribution is a special case of a normal distribution such that the mean is 0 and the standard deviation is 1.
What is the important similarity between the uniform and normal probability distribution?
They are both continuous, symmetric distribution functions.
What does the distribution look like if the mean mode and median are different?
If the mean, mode, and median are different, the distribution is likely skewed. For instance, if the mean is greater than the median, the distribution may be positively skewed (right-skewed), indicating a tail extending towards higher values. Conversely, if the mean is less than the median, the distribution may be negatively skewed (left-skewed), with a tail extending towards lower values. In both cases, the presence of outliers or a non-symmetrical spread can contribute to these differences.
Is Mean is more sensitive to skewness than the median?
If the distribution is positively skewed , then the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency (If it is a uni-modal distribution). If the distribution is negatively skewed then mean will always be the lowest estimate of central tendency and the mode will be the highest estimate of central tendency. In both positive and negative skewed distribution the median will always be between the mean and the mode. If a distribution is less symmetrical and more skewed, you are better of using the median over the mean.
