The Normal Distribution Is A Continuous, Unimodal And Symmetric Distribution

As discussed in the previous section, a normal distribution has particular characteristics it conforms to. i.e.

Standard deviation is a way of visualizing how spread out points of data are in a set. Using standard deviation helps to determine how rare or common an occurrence is. For example, data points falling within the boundaries of one standard deviation typically account for about 68% of data and those between (+/-)1 standard deviation and (+/-)2 standard deviations make about 27% combined. This can be better visualized by using a bell graph. Using the mean and standard deviation, the points where standard deviations occur can be drawn on the graph to better understand which data is rare and which is common.

We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So, we can get the standard deviation by:

Standard deviation is important in comparing two different sets of data that has the same mean score. One standard deviation may be small (1.85), where the other standard deviation score could be quite large (10)(Rumsey,

Theoretically from the recorded data the calculated mean, median, and mode will be the most accurate representation of the real world value. The difference between the highest recorded value and lowest recorded value is the range in the set of data. Standard deviation (s) is a quantity calculated to indicate an extend of deviation for a group of data as a whole (Marshall). This is calculated using:

Standard Deviation of Mean= 0.4762Standard Deviation of Median= 0.7539The standard deviation of the Mean is smaller, which means all of the data points will tend to be very close to the Mean. The Median with a larger Standard Deviation will tend to have data points spread out over a large range of values. Since the Mean has the smaller value of the Standard Deviations, it has the least variability.

and SD are _______________________ statistics. The mean is the measure of Central tendency of a distribution while SD is a measure of dispersion of its scores. Both X and SD is descriptive statistics.

Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.

5) Describe how the normal range for any given measurement is obtained. Explain why published values for normal ranges may differ and why these values must be continually checked and updated.

Sampling distribution of a sample statistics is the hypothetical distribution of the sample statistics of interest for a random sample, whereas the distribution of a sample is the probabilistic distribution of the ideas in the sample. The sampling distribution indicates how likely it is to get some definite sample when one draws a large amount of samples and the distribution of a sample shows how possible it is to get a particular data in a single random

21. Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.8 feet with a standard deviation of .5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of .6. Both women’s and men’s reach from this position is normally distributed. If this design is implemented:

standard deviation standardized value rescaling z-score normal model parameter statistic standard Normal model 68-95-99.7 Rule normal probability plot

1. Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions? It is a scores relationship to the mean indicating whether it is above or below the mean. It does this by converting scores to z score. Yes – keep going – just a bit more is needed.2 out of 3 pts

Ans: the random variable is being used in statistics and probability most of the time. This is also called stochastic or aleatory variable as his has an ability of making its values vary according to the subject or according to the chance that occur. A random variable has the ability of taking a set of different kind of values that also have the different value with the value associated with it.

Statistical dispersion is measured by a number system. The measure would be zero, if all the data were the same. As the data varies, the measurement number increases. There are two purposes to organizing this data. The first is to show how different units seem similar, by choosing the proper statistic, or measurement. This is called central tendency. The second is to choose another statistic that shows how they differ. This is known as statistical variability. The most commonly used statistics are the mean (average), median (middle or half), and mode (most frequent data). After the data is collected, classified, summarized, and presented, then it is possible to move on to inferential statistics if there is enough data to draw a conclusion.