Question

Descriptive Statistics

Using only the descriptive statistics provided, answer the following questions. Note, the scores are in a response to a 5-point Likert- type scale.
Example 1: Mean=3.45 Median=3.42
SD=.40
Describe the distribution of the data. Is this sample normally distributed, positively skewed, or negatively skewed? Why?
What two scores do 95.44% of the data fall between?
Example 2: Mean=4.00 Median=3.60
Describe the distribution of the data. Is this sample normally distributed, positively skewed, or negatively skewed? Why

Answer 1

The data in Example 1 appear nearly normally distributed but may show a slight positive skew. The data in Example 2 are positively skewed, as indicated by the mean being significantly higher than the median.

Step-by-step explanation:

Regarding Example 1, the distribution of the data can be inferred from the mean and median provided. With a mean of 3.45 and a median of 3.42 that are close in value and a standard deviation (SD) of 0.40, the distribution appears to be close to normal. However, if we notice a small difference, where the mean is slightly higher than the median, it can hint towards a slight positive skew in the data, but it is almost negligible. For a normally distributed data set, approximately 95.44% of the data falls within two standard deviations from the mean. To calculate this range, we use the formula: mean ± 2*SD. Thus, for Example 1, two scores that 95.44% of the data fall between are 3.45 ± 0.80 (which is 3.45 ± 2*0.40), so the interval is 2.65 to 4.25.

Concerning Example 2, with a mean of 4.00 and a median of 3.60, the larger difference between the two suggests that the distribution is skewed. Since the mean is higher than the median, this indicates a positive skew. Without additional measures, such as the mode and standard deviation, we can't provide the exact range that covers 95.44% of the data, but it's clear from the provided statistics that the skewness is positive.