What does the mean and standard deviation tell us about data?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

What does the mean tell us in statistics?

The mean, also referred to by statisticians as the average, is the most common statistic used to measure the center of a numerical data set. The mean is the sum of all the values in the data set divided by the number of values in the data set.

Why is the mean better than the median?

Unlike the mean, the median value doesn’t depend on all the values in the dataset. Consequently, when some of the values are more extreme, the effect on the median is smaller. When you have a skewed distribution, the median is a better measure of central tendency than the mean.

Which set of data has the smallest standard deviation?

The smallest standard deviation possible in a distribution is 0. This occurs when each element of the distribution is the same. A deviation is a data point’s distance from the distribution mean. If all points in the distribution are the same, then the mean is the same as each distribution point.

What is a small standard deviation?

Basically, a small standard deviation means that the values in a statistical data set are close to the mean (or average) of the data set, and a large standard deviation means that the values in the data set are farther away from the mean.

Which measure of central tendency is affected by extreme values?

The mean
The mean is the measure of central tendency most likely to be affected by an extreme value. Mean is the only measure of central tendency which depends on all the values as it is derived from the sum of the values divided by the number of observations.

Does the mean represent the center of the data?

the mean represents the center of a numerical data set. to find the mean, sum the data values & then divide by the number of values in the data set.

What does it mean when mean and median are different?

When in doubt, ask for both median and mean – if they are significantly different, that tells you that your data set is probably skewed in one direction or another and could affect your decisions.

What measure of central tendency is easily affected by extreme scores?

So the median is a better measure of the central tendency. Extreme scores strongly affect the mean, but not the median.

What measure of variation is easily affected by the extreme scores?

The range is easy to calculate but it is very much affected by extreme values. Like the range, the IQR is a measure of variability, but you must find the quartiles in order to compute its value. The interquartile range is the difference between upper and lower quartiles and denoted as IQR.

What is the difference between sample mean and population mean?

“Sample mean” (all you’ve got) vs. population mean -or (theoretical) probability distribution mean. True mean, here, refers to population mean . Where as mean refers to sample mean. Sample is a subset of population.

Why is the standard deviation smaller when data is spread out?

When the values in a dataset are grouped closer together, you have a smaller standard deviation. On the other hand, when the values are spread out more, the standard deviation is larger because the standard distance is greater. Conveniently, the standard deviation uses the original units of the data, which makes interpretation easier.

What is the difference test in statistics?

It is a statistical test of the difference of means for two or more groups. box-plot – Summary plot based on the median, quartiles, and extreme values. The box represents the interquartile range which contains the 50\% of values. The whiskers represent the range; they extend from the box to the highest and lowest values, excluding outliers.

What is the difference between true mean and sample mean?

True mean, here, refers to population mean . Where as mean refers to sample mean. Sample is a subset of population. For Ex. Suppose we want to take a survey from a certain region which contains approx 1,00,000.