PSY 201 1Introduction to Statistics in Psychology: PSY 201Greg Francis, PhDDepartment of Psychological SciencesPsychological Sciences Building, Room 3174(765) 494-6934email: [email protected]://www1.psych.purdue.edu/∼gfrancis/Classes/PSY201/Homework 2Due: 01 September 2010Hand in your answers on a separate sheet of paper.(1) A class of students recorded the number of years their families had lived in their town. Hereare two graphs that students drew to summarize the data. Which graph gives a more accuraterepresentation of the data? Why?(2) Using the following distribution of scores, find the percentile rank corresponding to X = 7.0.X f10 29 88 47 66 45 1(3) Using the following distribution of scores, find the 50th percentile.X f20–24 215–19 310–14 35–9 100–4 2PSY 201 2(4) For the following set of N = 20 scores, construct a frequency distribution table using an intervalwidth of 5 points.14, 8, 27, 16, 10, 22, 9, 13, 16, 12, 10, 9, 15, 17, 6, 14, 11, 18, 14, 11(5) Find each value requested for the distribution of scores in the following table.a) nb)PXic)PX2iX f5 14 23 42 31 1(6) The following frequency distribution presents a set of exam scores for a class of N = 20 students.X f cf c%90–99 4 20 10080–89 7 16 8070–79 4 9 4560–69 3 5 2550–59 2 2 10a) Find the 30th percentile.b) Find the 88th percentile.c) What is the percentile rank for X = 77?d) What is the percentile rank for X = 90?(7) Mental imagery has been shown to be very effective for improving memory. In one demonstra-tion study, two groups of participants were presented with a list of 20 words. One group was giveninstructions to use mental images to help them remember the words, and the second group wasgiven no special instructions. After the list was presented, each person was asked to recall as manywords as possible. The scores for the two groups are as follows:Imagery group: 18, 19, 18, 17, 19, 13, 20, 17, 18, 18, 20, 18, 14, 19, 16No-instruction group: 11, 12, 16, 12, 10, 13, 14, 12, 10, 8, 13, 10, 11, 14, 12a) Sketch a histogram showing the distribution of scores for each group (two separate graphs).b) Describe each group by identifying the shape of the distribution and the approximate centerof the distribution.c) Based on the appearance of the two distributions, what is the effect of using mental imageson the level of performance for this memory task.PSY 201 3(8) For the following set of scores2, 3, 2, 4, 5, 2, 4, 2, 1, 7, 1, 3, 3, 2, 4, 3, 2, 1, 3, 2a) Construct a frequency distribution table.b) Sketch a polygon showing the distribution.c) Describe the distribution using the following characteristics:i) What is the shape of the distribution?ii) What score best identifies the center (average) for the distribution?iii) Are the scores clustered together, or are they spread out across the scale?(9) A survey given to a sample of 200 college students contained questions about the followingvariables. For each variable identify the kind of graph that should be used to display the distributionof scores (histogram, polygon, or bar graph). Justify your choice with one or two sentences.a) number of pizzas consumed during the previous week.b) size of T-shirt worn (S, M, L, XL).c) gender (male/female)d) grade point average for the previous semester.e) college class (freshman, sophomore, junior, senior)(10) Using the following frequency distribution, find each of the percentiles and percentile ranksrequested:X f cf c%95–99 2 50 10090–94 5 48 9685–89 12 43 8680–84 15 31 6275–79 10 16 3270–74 2 6 1265–69 2 4 860–64 1 2 450–59 1 1 2a) Find the 30th percentile.b) Find the 80th percentile.c) Find the percentile rank of X = 60.d) Find the percentile rank of for X =