Question

Consider the following list of quiz scores. 2, 4, 6, 7, 7, 7, 8, 9, 10, 10 The mean score is 7. a) Two more students take the quiz. If the mean score stays at 7, which of the following is a possible list of the 2 additional quiz scores? b) Which of the following is a reasonable estimate for the standard deviation in quiz score based off of the original ten scores? c) The teacher accidentally recorded one of the original scores wrong. The 2 should really be another 7. If the teacher deletes the 2 and replaces it with another 7, what will happen to the mean and standard deviation? The new mean will and the standard deviation

Answer 1

There are 10 scores  2, 4, 6, 7, 7, 7, 8, 9, 10, 10

a)

mean =7

after adding 2 new scores then mean is also 7

now in this case number of observations =10+2=12

so for mean =7 sum of scores =7*12 =84

while for n=10 sum =10*7=70

so sum of new scores should be equal to 84-70=14 so any two numbers with sum =14 will be 2 news scores

b)

sample standard deviation is estimate of population standard deviation which is given by

=2.54

c)

sum of 10 observations =70

now replace 2 by 7 gives sum =70-2+7=75

so new mean =75/10 =7.5

so mean increases while

SD becomes 1.91 hence SD decreases as we replaced 2 by 7