04A Quiz

What is the interquartile range for the following scores? 2, 5, 9, 12, 18, 22, 45

17

If the variance for a group of scores equals 25, what is the standard deviation?

5

Consider a normal distribution with over 1,000 values. What percentage of values are within one standard deviation of the mean? This includes the values from one standard deviation below the mean to one standard deviation above the mean.

68%

Consider a normally distributed population of scores, where the mean is 50 and the standard deviation is 20. What percentage of scores are between 30 and 70?

68%

Consider a positively skewed distribution with a mean of 80 and a standard deviation of 16. What percentage of scores are between 64 and 96?

68% of the population is within one standard deviation of the mean, and that 95% is within two standard deviations of the mean. However, we are told that the distribution was Positively Skewed.... so we can't apply the Empirical Rule to help us out here. The Empirical Rule is only helpful when describing a normal distribution. For a non-normal distribution (skewed, bi-modal, flat, etc), the rule would be misleading. So, always check that the distribution is normally distributed before applying the Empirical Rule.

Consider a normally distributed population of scores, where the mean is 100 and the standard deviation is 16. Approximately what percent of scores will be between 84 and 116?

95%

When the measure of central tendency is the median, and you are concerned about outliers, which of the following is the most appropriate measure of variability?

Both the range and the standard deviation are affected by extreme values. Only the interquartile range is unaffected by extreme values (since it reports the range for the middle 50% of the values - from the 25th percentile to the 75th percentile).

What is the variance for the scores 1, 3, 3, 5?

To calculate the variance, first determine the mean. In this case the mean is 3.Next, square the difference between the mean and each score (1-3=2; 2 squared is 4; do this for each score).Last, add up the squared difference scores, & divide by the number of scores.

A frequency histrogram of a distribution with a negative skew will have a tail pointing toward the

left. A normal distribution is symmetrical (both sides look the same). A positively skewed distribution has its tail pointing to the right.