Solutions - Chapter 4 - page 428
Chapter 4: Variability
1. a. The range is 7 points and the interquartile range is 2 points (from 2.5 to 4.5).
b. The range is 27 points and the interquartile range is 2 points (from 2.5 to 4.5).
c. The range is completely determined by the extreme scores. The interquartile range is not
influenced by the most extreme scores.
2. a. SS is the sum of squared deviation scores.
b. Variance is the mean squared deviation.
c. Standard deviation is the square root of the variance. It provides a measure of the
standard distance from the mean.
3. The standard deviation, σ = 20 points, measures the standard distance between a score and
the mean.
4. SS cannot be less than zero because it is computed by adding squared deviations. Squared
deviations are always greater than or equal to zero.
5. A standard deviation of zero indicates there is no variability. In this case, all of the scores in
the sample have exactly the same value.
6. A standard deviation of s = 5 indicates that the scores are scattered around the mean with the
average distance between X and M equal to 5 points. More specifically, around 70% of the
scores should be within 5 points of the mean and about 95% of the scores should be within 10
points of the mean.
7. a. The range is 5 points, the interquartile range is 1 point (from 2.5 to 3.5), and the standard
deviation is √1.25 = 1.12.
b. After adding two points to every score, the range is still 4, the interquartile range is still
1,
and the standard deviation is still 1.12. Adding a constant to every score does not affect
variability.
8. An unbiased estimate means that on average the sample statistic will provide an accurate
representation of the corresponding population parameter. More specifically, if you take all the
possible samples and compute the variance for each sample, then the average of all the sample
variances will be exactly equal to the population variance.
9. a. Median = 3.5. Semi-interquartile range = 2 (Q1 = 2.5 and Q3 = 6.5)
b. The median is still 3.5 and the semi-interquartile range is still 2 points.
c. One extreme score does not influence the median or the semi-interquartile range.
