# Interpreting standard deviation and mean relationship

### Standard deviation - Simple English Wikipedia, the free encyclopedia

Consequently, if we know the mean and standard deviation of a set of In column (2) the difference between each reading and the mean is recorded. The sum. The average (mean) and the standard deviation of a. The following article is intended to explain their meaning and provide additional They are often referred to as the "standard deviation of the mean" and the " standard error of the mean. It describes the distribution in relation to the mean.

Then, you can create the graph with groups to determine whether the group variable accounts for the peaks in the data. Simple With Groups For example, a manager at a bank collects wait time data and creates a simple histogram. The histogram appears to have two peaks. After further investigation, the manager determines that the wait times for customers who are cashing checks is shorter than the wait time for customers who are applying for home equity loans.

The manager adds a group variable for customer task, and then creates a histogram with groups.

Look for outliers Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot. However, a team with a high standard deviation might be the type of team that scores many points strong offense but also lets the other team score many points weak defense. Trying to know ahead of time which teams will win may include looking at the standard deviations of the various team "statistics.

In racingthe time a driver takes to finish each lap around the track is measured. A driver with a low standard deviation of lap times is more consistent than a driver with a higher standard deviation.

This information can be used to help understand how a driver can reduce the time to finish a lap. Money[ change change source ] In money, standard deviation may mean the risk that a price will go up or down stocks, bonds, property, etc. It can also mean the risk that a group of prices will go up or down [3] actively managed mutual funds, index mutual funds, or ETFs.

Risk is one reason to make decisions about what to buy. Risk is a number people can use to know how much money they may earn or lose. As risk gets larger, the return on an investment can be more than expected the "plus" standard deviation.

### Interpret the key results for Descriptive Statistics - Minitab Express

However, an investment can also lose more money than expected the "minus" standard deviation. For example, a person had to choose between two stocks. Stock A over the past 20 years had an average return of 10 percent, with a standard deviation of 20 percentage points pp.

Stock B over the past 20 years had an average return of 12 percent but a higher standard deviation of 30 pp. The coefficient of variation is adjusted so that the values are on a unitless scale. Because of this adjustment, you can use the coefficient of variation instead of the standard deviation to compare the variation in data that have different units or that have very different means.

Interpretation The larger the coefficient of variation, the greater the spread in the data. For example, you are the quality control inspector at a milk bottling plant that bottles small and large containers of milk. You take a sample of each product and observe that the mean volume of the small containers is 1 cup with a standard deviation of 0. Although the standard deviation of the gallon container is five times greater than the standard deviation of the small container, their coefficients of variation support a different conclusion.

In other words, although the large container has a greater standard deviation, the small container has much more variability relative to its mean. For this ordered data, the first quartile Q1 is 9.

## Standard deviation

Histogram, with normal curve A histogram divides sample values into many intervals and represents the frequency of data values in each interval with a bar. Interpretation Use a histogram to assess the shape and spread of the data.

Histograms are best when the sample size is greater than You can use a histogram of the data overlaid with a normal curve to examine the normality of your data. A normal distribution is symmetric and bell-shaped, as indicated by the curve. It is often difficult to evaluate normality with small samples. A probability plot is best for determining the distribution fit.

**Sec 3.2: Interpret a standard deviation**

Good fit Poor fit Individual value plot An individual value plot displays the individual values in the sample. Each circle represents one observation.

An individual value plot is especially useful when you have relatively few observations and when you also need to assess the effect of each observation.

Interpretation Use an individual value plot to examine the spread of the data and to identify any potential outliers.