a statistics problem....help.......?

Question

All students in the physical education class completed a basketball free-throw shooting event and the highest number of shots made was 32. The next day a student transferred into the school and completed the event, making 35 shots. Indicate whether adding the new student's score to the rest of the data made each of these summary statistics increase, decrease, or stay about the same.
a. mean
b. median
c. range
d. IQR
e. standard deviation

Answer 1

The answer depends on the size of the class.

a. The mean certainly will increase -- but if it is a large class, it will stay about the same.

b. The median will not decrease -- it could increase or could stay the same. For example, if the previous scores were 10, 20, 20, 32 -- then it would stay the same. It they were 10-20-30-32 then they would increase. If the class is big, it could increase, but probably not by much.

c. Range -- For this one, the answer is unambiguous -- the range increases with the top end changing from 32 to 35

d -- the ranges of the first three quarters will not change much if it is a big class -- but could change quite a bit for a small class. The high ranges can not decrease. The high end of the top quartile range will increase from 32 to 35. The bottom end of the range could go up higher, too.

e. The answer here is similar to the answer for the mean. The s.d. has to increase -- but if it is a large class, the increase will be small.

Answer 2

a) the mean will increase, only slightly. we know this because 35 is the new high and will bring the mean up. how much is going to be a function of the number of other students.

b) the median will either stay the same or increase. for example, say there were 12 students before the transfer. the median would be the average of the 6th and 7th data points in the set and if these two data points were equal then when the transfer student moved in and became the 13th data point, the median would be the 7th data point, equal to the original. if the median was less than the the value of the 7th data point because the 6th and 7th data points were unequal before the transfer then after the transfer the median will increase.

c) the range will increase. say the low was 4 and the old high score was 32. the range was 28. now that the new transfer kid is there the range is 35 - 4 = 31.

d) the IQR will most likely not change. adding one data point may not move the quartiles. if you use weighted averages to determine the quantiles it may or may not increase. you could even conceivably see a decrease. It will be a function of the data set and size.

e) the standard deviation will increase as the spread of the data as been increased.

Answer 3

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