Measures of Central Tendency, Measures of Dispersion, Location of Scores<\/p>\n
Measures of Central Tendency<\/p>\n
1.\tFind the mean, median, and mode for each of the following sets of scores (3 points per set).<\/p>\n
a.\t3, 4, 4, 6, 6, 6, 6, 7, 7, 9, 9<\/p>\n
b.\t6, 8, 5, 5, 8, 9, 6, 28<\/p>\n
c.\t20, 22, 22, 24, 24, 27, 28, 28, 31<\/p>\n
d.\t-3, -2, 0, 1, -3, -5, 3, 6, 3, 5, -1<\/p>\n
2.\tIn which of the sets of scores in question #1 is the mean a poor measure of central tendency? Why? (2 points)<\/p>\n
3.\tIn which of the sets of scores in question #1 is the mode a poor measure of central tendency? Why? (2 points)<\/p>\n
4.\tWhat can we say about the relationship between the mean and median is a positively skewed distribution? In a negatively skewed distribution? (2 points)<\/p>\n
5.\tCalculate the mean of the following set of scores: \t3, 1, 3, 4, 5, 5, 7, 9 (3 points each)<\/p>\n
a.\tAdd a constant (c=3) to each score and recalculate the mean. In general, what is the effect on the mean when any constant is added to all the scores?<\/p>\n
b.\tSubtract a constant (c=3) from each score and recalculate the mean. In general, what is the effect on the mean when any constant is subtracted from all the scores?<\/p>\n
c.\tMultiply each score by a constant (c=3). Recalculate the mean. In general, what is the effect on the mean when each score is multiplied by any constant?<\/p>\n
d.\tDivide each score by a constant (c=3). Recalculate the mean. In general, what is the effect on the mean when each score is divided by any constant?<\/p>\n
6.\tYou have calculated the maximum speed of various race cars. You later discover that all the speedometers were set 5 miles an hour too slow. How will adjusting the speedometers affect the mean, median, and mode of the speeds? (2 points)<\/p>\n
Measures of Dispersion<\/p>\n
7.\tFor the following sets of scores, calculate the sum of squares, the variance, and the standard deviation (4 points each).<\/p>\n
a.\t2, 4, 7, 3, 9, 10, 27<\/p>\n
b.\t7, 7, 7, 7, 7, 7, 7, 7, 7, 7<\/p>\n
c.\t3, 5, 6, 7, 8, 9, 10, 11<\/p>\n
8.\tWhy is the standard deviation in part a of question #7 so large? Describe the effects of extreme deviations on the standard deviation (2 points).<\/p>\n
9.\tDetermine the range for each of the set of measurements in question #7. For which of these is the range a misleading index of variability and why (2 points)?<\/p>\n
10.\tCalculate s2 and s for the following set of scores: 3, 5, 9, 3, 8, 2, 6 (4points per set)<\/p>\n
a.\tAdd a constant (c=2) to each score and recalculate s2 and s. In general, what is the effect on these statistics when any constant is added to all scores?<\/p>\n
b.\tSubtract a constant (c=2) to each score and recalculate s2 and s. In general, what is the effect on these statistics when any constant is subtracted from all scores?<\/p>\n
c.\tMultiply each score by a constant (c=2) and recalculate s2 and s. In general, what is the effect on these statistics when all scores are multiplied by a constant?<\/p>\n
d.\tDivide each score by a constant (c=2) and recalculate s2 and s. In general, what is the effect on these statistics when all scores are divided by a constant?<\/p>\n
11.\tOne sample has a mean of M = 12 and a second sample has a mean of M = 10. The two samples are combined into a single set of scores. (2 points each)<\/p>\n
a.\tWhat is the mean for the combined set if both of the original samples have n = 7 scores?<\/p>\n
b.\tWhat is the mean for the combined set if the first sample has n = 3 and the second sample has n = 7?<\/p>\n
c.\tWhat is the mean for the combined set if the first sample has n = 7 and the second sample has n = 3?<\/p>\n
\n12.\tFor a population with ? = 70 and s = 16<\/p>\n
a.\tthe z-score for each of the following X values (1 point each)<\/p>\n
i.\tX = 75
\nii.\tX = 62
\niii.\tX = 54.5
\niv.\tX = 92.3<\/p>\n
\nb.\tthe score (X value) that corresponds to each of the following z-scores (1 point each)<\/p>\n
i.\tz = -.35
\nii.\tz = 1.00
\niii.\tz = -2.00
\niv.\tz = .67<\/p>\n
\nc.\tthe proportion of the normal distribution that is located below the following
\nz-scores (1 point each)<\/p>\n
i.\tz = -.35
\nii.\tz = 1.00
\niii.\tz = -2.00
\niv.\tz = .67<\/p>\n
\nd.\tthe proportion of the normal distribution that is located above the following z-scores (1 point each)<\/p>\n
i.\tz = -.55
\nii.\tz = 1.00
\niii.\tz = -2.00
\niv.\tz = 1.50<\/p>\n
\ne.\tthe proportion of the normal distribution that is located between the two z-score values (2 points each)<\/p>\n
i.\tz = .75 and z = 1.50
\nii.\tz = -0.50 and z = 0.75
\niii.\tz = -2.00 and z = -0.50<\/p>\n
\n13.\tA fifth grader takes a standardized achievement test (?= 125, s = 15) and scores a 144. What percentage of children score below this fifth grader? (2 points)<\/p>\n
14.\tPat and Chris both took a spatial abilities test (? = 80, s = 8). Pat scored a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris? (2 points)<\/p>\n
2.\tScores on the SAT form a normal distribution with ? = 500 and s = 100.<\/p>\n
a.\tWhat is the minimum score necessary to be in the top 10% of the SAT distribution? (2 points)<\/p>\n
b.\tFind the range of values that defines the middle 90% of the distribution of SAT scores. (2 points)<\/p>\n","protected":false},"excerpt":{"rendered":"
Measures of Central Tendency, Measures of Dispersion, Location of Scores Measures of Central Tendency 1. Find the mean, median, and mode for each of the following sets of scores (3 points per set). a. 3, 4, 4, 6, 6, 6, Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-4873","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/4873","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=4873"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/4873\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=4873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=4873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=4873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}