What is Standard Deviation?
A standard deviation is a quantity that shows the degree of variation of a set of data values. A low standard deviation shows that data points are close to the mean. A high standard deviation is certainly different. Rather, a high standard deviation shows that data points are spread over a wide range of values.
What is Normal Probability Curve?
Most noteworthy, the curve of normal probability is bell-shaped. It shows the probability distribution of a continuous variable. Furthermore, this curve shows a normal distribution. Also, the total area under it shows the sum of all probabilities for a random variable. Therefore, the area under the curve is one. This has a normal curve with mean=0 and standard deviation=1.
Standard Deviation with Reference to Normal Probability Curve
Relationship Between Standard Deviation and Normal Probability Curve
Normal probability curve is the distribution of values around the mean of a population. The population is evenly distributed. The standard deviation is the calculation of the width of that curve based on sample value. Also, the standard deviation is commonly used in a simple form. The standard deviation shows a certain range of the population included. There is no reason to restrict to those values.
The way to define a probability curve is in two ways. One is the mean and the other is a standard deviation. 68% of the area of a normal probability curve is within one standard deviation of the mean. Almost 95% of the area of a normal probability curve is within two standards deviations of the mean.
Interpretation of Standard Deviation
The values of data set in small standard deviation are close to the mean. In contrast, in large standard deviation values are far away from the mean.
A small standard deviation is a goal in certain situations. So, the situation can be where the results are small. An example can be quality control in production. Hence a very small car part should not have a big standard deviation. Furthermore, a big standard deviation means that lots of parts end in the trash. This is because they don’t fit right with the car.
Probably, often situations come where one just observes and records data. In such situations, a large standard deviation is certainly not a bad thing. It shows a large amount of variation in the group. An example can be the salaries of everyone in a company. This varies from the salary of a laborer to the CEO. Therefore, in this case, the standard deviation would be very high.
Following are some properties which are helpful in interpreting standard deviation:
- The standard deviation can certainly never be a negative number.
- The smallest value for any standard deviation is certainly zero. This happens when every number in the data set is exactly the same.
- The basis of standard deviation is on distance from the mean. Due to this, extremely low or high numbers in the data set can affect it.
- Consequently, this deviation has the same units as the original data.