Question: A psychological test is available to evaluate a student’s motivation, study habits and attitudes toward school. All incoming students at a particular school are given this test. A random sample of 18 students from the school provided the following scores:

70 139 128 121 110 101 133 136 123

127 112 128 111 118 103 114 129 148

a) Construct a stem and leaf display for these data using the last digit of each number as the leaf. Place the leaves in ascending order.

b) Calculate the quartiles and interquartile range.

c) Sketch a box and whisker plot. Indicate any other outlines

d) Within what range did the middle 50% of the students score?

e) What is the percentile rank of the student who scored 136 on the test? What does this number tell you?

f) Calculate the (approximate) value of the 60^th percentile. What does this number tell you?

g) Using the sample data in ungrouped form, calculate the mean of the student scores

h) Using the sample data in the ungrouped form, calculate the standard deviation of the student scores. Use the short cut formal.

i) Does the data have a mode? If so, what is it?

j) Considering the relationship among the mean, median, and mode, does this data exhibit skewness? If so in what direction?