Table of Contents
- 1 What is an example of when you would want a small standard deviation?
- 2 What makes a small standard deviation?
- 3 When would you want a small standard deviation?
- 4 When the standard deviation is small the curve is?
- 5 Which dataset has lowest standard deviation?
- 6 What is the largest possible standard deviation?
What is an example of when you would want a small standard deviation?
This generally implies that your data don’t change a lot. For example, if you take an exam for several times, and your scores give a small standard deviation, you can declare that you perform stably (either well or badly) on the series of exams. In a two-dimensional example, you shoot towards a round target with rings.
What makes 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. The second data set isn’t better, it’s just less variable.
Which set of scores has the smallest standard deviation Why?
145, 143, 145, 147 (has the smallest standard deviation, because the variability among these four scores is much less than the variability within any of the other sets of scores.) A sample of n=10 scores is selected from a population.
What is 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.
When would you want a small standard deviation?
A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
When the standard deviation is small the curve is?
99.7\% of the data falls within three standard deviations of the mean. The standard deviation controls the spread of the distribution. A smaller standard deviation indicates that the data is tightly clustered around the mean; the normal distribution will be taller.
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.
Which histogram has the smallest standard deviation?
To begin to understand what a standard deviation is, consider the two histograms. Histogram 1 has more variation than Histogram 2. In the first histogram, the largest value is 9, while the smallest value is 1. The overall range of data is 9 – 1 = 8….Standard Deviation.
| Length (X) | Deviation from Average (X- X) |
|---|---|
| 8 | 8 – 4.8 = 3.2 |
Which dataset has lowest standard deviation?
Whilst all the values in set B are relatively close to the mean, set A’s values are all within one of the mean. Five of the values are 41, one of the values is 42, and the mean is 41.16 recurring. This means that set A would have the lowest standard deviation as the variation from the mean is lowest.
What is the largest possible standard deviation?
For question (b) there is only one correct answer, which is 0, 0, 10, 10. Here are five different sets of four numbers. As you can see, the set {0, 0, 10, 10} does have the largest possible standard deviation.
What does 1 standard deviation represent?
Using the standard deviation, statisticians may determine if the data has a normal curve or other mathematical relationship. If the data behaves in a normal curve, then 68\% of the data points will fall within one standard deviation of the average, or mean, data point.