a study was conducted to investigate whether music training has an influence on
ID: 3073651 • Letter: A
Question
a study was conducted to investigate whether music training has an influence on the ability to memorize. the comparative box plots for the data sets are shown below. Exam 1 was conducted to investiage whether musictraining has an infuence on t orize. The comparitve box plots for the data sets are shown below. 1. (12 points) A study ability to mem to i of items zed by people with or witthout music training Music a. Which of the data sets has the largest IQR? b. Which data set is skewed right? c. In which data set is the mean smaller than the No MusicMusic No Music Music No Music Music Median? items. d. Approximately 25% of the people with training memorize less than Approximately 75% of the people with no music training memorize at least- items The appropriate measure of spread for the No Music data is: e. - f.Explanation / Answer
a) The IQR is measured by the width of the box.
IQR Music = 10 - 6 = 4
IQR No Music = 8 - 5 = 3
Thus IQR for Music is the largest.
b) A dataset is skewed right when the right handside of the median is longer than the left hand side.
Thus, No Music data is right skewed.
c) The mean is smaller than the median in the left skewed data.
Music data is left skewed and has the mean smaller than the median.
d) The box plot is divided into quartiles such that the box region forms the IQR. The first quartile i.e. 25% of the data is present from the lower end of the tail (whisker) to the starting point of the box.
Thus, for Music data set, approx 25% of the people memorise less than 6 items.
e) 75% is represented by the region from the median to the end point of the box plot.
Thus, 75% of the people with no training memorise at least 6 items.
f) The measure of spread for boxplot is the range of the data.
Thus, for no music data the spread is 11-4 = 7
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