Question

True or False: a.) Variance is the mean of the squared deviation score. b.) For any population, a z-score of +1.00 corresponds to a location above the mean by one standard deviation. c.) In a distribution with s=8, a score of X=64 corresponds to z=-.50. The mean for this sample will be M=60. d.) Transforming X values into z-scores will not change the shape of the distribution. e.) One advantage of transforming X values into z-scores is that the transformation always creates a normal shaped distribution. f.) It is possible for more than half of the scores in a distribution to have values greater than the mean. g.) A distribution with a mean u=50 and a median of 70 probably is positively skewed.

Answer 1

Solution:-

a) True- Variance is the mean of the squared deviation score.

b) True -  For any population, a z-score of +1.00 corresponds to a location above the mean by one standard deviation.

c) False - In a distribution with s = 8, a score of X = 64 corresponds to z =-.50. The mean for this sample will be M = 60.

x = 64

By applying normal distruibution:-

z = 0.50

Hence z is not equal to - 0.50.

d) True - Transforming X values into z-scores will not change the shape of the distribution.

e) False - One advantage of transforming X values into z-scores is that the transformation always creates a normal shaped distribution.

f) True - It is possible for more than half of the scores in a distribution to have values greater than the mean.

g) False - A distribution with a mean u=50 and a median of 70 probably is positively skewed.

In a positively skewed distribution the median is less than the mean.