Question

Determine whether each of the following statements is true or false, and explain why in a few sentences.

1. The mean, median, and mode of a normal distribution are all equal.

2. If the mean, median, and mode of a distribution are all equal, then the distribution must be a normal distribution.

3. If the means of two distributions are equal, then the variance must also be equal.

4. The sample mean is not the same as the population mean.

5. The mode of a distribution is the middle element of the distribution.

6. A large variance indicates that the data are grouped closely together.

Answer the following questions in a few sentences.

7. What is meant by the range of a distribution?

8. How are the variance and the standard deviation of a distribution related? What is measured by the standard deviation?

9. Describe the characteristics of a normal distribution.

10. What is meant by a skewed distribution?

Answer 1

1. The mean, median, and mode of a normal distribution are all equal.

True

The mean, median, and mode of a normal distribution are equal. The area under the normal curve is equal to 1.0.

2.If the mean, median, and mode of a distribution are all equal, then the distribution must be a normal distribution.

True

The midpoint of the normal distribution is also the point at which three measures fall: themean, median, and mode. In a perfectly normal distribution, these three measures are all the same number.

3. If the means of two distributions are equal, then the variance must also be equal.

False

4. The sample mean is not the same as the population mean.

True

The sample mean is mainly used to estimate thepopulation mean when population mean is notknown as they have the same expected value.

5. The mode of a distribution is the middle element of the distribution

False

Median is the central tendency of distribution. Mode is the most common value among the given observations

6. A large variance indicates that the data are grouped closely together.

A high variance indicates that the data points are very spread out from the mean, and from ... A low standard deviation indicates that the data points tend to be very close to the mean.

7. What is meant by the range of a distribution?

The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

8. How are the variance and the standard deviation of a distribution related? What is measured by the standard deviation?

The variance and the closely-related standard deviation are measures of how spread out a distribution is. In other words, they are measures of variability.

The standard deviation is a measure of how spread out the numbers in a distributionare.

variance and standard deviation are both measures of variation for interval-ratio variables.

9. Describe the characteristics of a normal distribution.

There are four characteristics of a normal distribution. Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equal.

10. What is meant by a skewed distribution?

Skewed distributions are asymmetrical and have data that clusters toward one end.

A distribution is said to be skewed when the data points cluster more toward one side of the scale than the other,

A distribution is negatively skewed if the scores fall toward the higher side of the scale and there are very few low scores.

A distribution is positively skewed if the scores fall toward the lower side of the scale and there are very few higher scores.