Question

Which statement is true concerning a normally distributed data set?

50% of data = 1 Std. Deviation

Median=Range=Std. Deviation

Mean=Median=Mode

Std. Deviation= Range

Answer 1

1.50% of data = 1 Std. Deviation False

Reason:-

Distribution

• Probabilities of the Standard Normal Distribution Z
• Normal Probability Calculator
• Z-Scores with R
• Probability for a Range of Values

Contents

All Modules

Table of Z Scores

The Standard Normal Distribution

The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation. For the standard normal distribution, 68% of the observations lie within 1 standard deviation of the mean; 95% lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean. To this point, we have been using "X" to denote the variable of interest (e.g., X=BMI, X=height, X=weight). However, when using a standard normal distribution, we will use "Z" to refer to a variable in the context of a standard normal distribution. After standarization, the BMI=30 discussed on the previous page is shown below lying 0.16667 units above the mean of 0 on the standard normal distribution on the right.

2.Median=Range=Std. Deviation

For a perfectly normal distribution, the values of the mean, median and mode are all equal. For a perfectly normal distribution, there is no relationship between the value of the mean and standard deviation (any mean can be accompanied by any standard deviation value.

3.Mean=Median=Mode false

To find the mean, add up the values in the data set and then divide by the number of values that you added. To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list. To find the mode, identify which value in the data set occurs most often.

4.Std. Deviation= Range

A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.