# What can you conclude from the mean and standard deviation?

## What can you conclude from the mean and standard deviation?

More precisely, it is a measure of the average distance between the values of the data in the set and the mean. A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values.

How can you conclude that the data is normally distributed?

A normal distribution is symmetric about the mean. So, half of the data will be less than the mean and half of the data will be greater than the mean. Therefore, 50\% percent of the data is less than 5 .

What do the mean and standard deviation tell you about a data set?

It tells you, on average, how far each score lies from the mean. In normal distributions, a high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean.

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### How do you tell if data is normally distributed or skewed?

In a normal distribution, the mean and the median are the same number while the mean and median in a skewed distribution become different numbers: A left-skewed, negative distribution will have the mean to the left of the median. A right-skewed distribution will have the mean to the right of the median.

What is the relationship between mean and standard deviation?

The standard deviation is calculated as the square root of variance by determining each data point’s deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

What does it mean if standard deviation is close to the mean?

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.

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#### When mean and standard deviation are equal?

One situation in which the mean is equal to the standard deviation is with the exponential distribution whose probability density is f(x)={1θe−x/θif x>0,0if x<0. The mean and the standard deviation are both equal to θ. for all positive numbers x and y.

What is difference between standard deviation and mean deviation?

Standard deviation is basically used for the variability of data and frequently use to know the volatility of the stock. A mean is basically the average of a set of two or more numbers. Mean is basically the simple average of data. Standard deviation is used to measure the volatility of a stock.

What does the standard deviation tell us about the distribution?

We’ll return to the rule soon. The Normal Curve tells us that numerical data will be distributed in a pattern around an average (the center line). Standard deviation is considered the most useful index of variability. It is a single number that tells us the variability, or spread, of a distribution (group of scores).

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## What is the range of the distribution when the distribution is normal?

When a distribution is normal, then 68\% of it lies within 1 standard deviation, 95\% lies within 2 standard deviations, and 99\% lies with 3 standard deviations. So, 68\% of the time, the value of the distribution will be in the range as below, Upper Range = 65+3.5= 68.5 Lower Range = 65-3.5= 61.5

How do you calculate standard deviation from mean and square root?

Step 1: Compute the mean for the given data set. Step 2: Subtract the mean from each observation and calculate the square in each instance. Step 3: Find the mean of those squared deviations. Step 4: Finally, take the square root obtained mean to get the standard deviation.

Can standard deviation be negative?

Interestingly, standard deviation cannot be negative. A standard deviation close to indicates that the data points tend to be close to the mean (shown by the dotted line). The further the data points are from the mean, the greater the standard deviation.