Explanation:
let's first sort the data points from low to high :
42, 68, 70, 72, 74, 75, 79, 80, 82, 83, 84, 85, 86, 87, 91, 92, 94, 95, 97, 98
67.
the mean score is the sum of all data points divided by the number of data points :
1634/20 = 81.7
=> BC is correct
68.
the median is the number in the sorted list, what half of the data points are lower, and the other half higher.
in case of an even number of data points, it is the mean value of the 2 central data points.
in our case these are 83 and 84. the mean value between these two numbers is 83.5.
=> BE is correct
69.
the mode is the most frequent number among the data points.
but all scores appear only once.
so, some say, the mode is the set of all data points.
or, others say, there is no mode (like your teacher, apparently)..
=> ABC is correct.
70.
mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean.
so, now we are creating a new data set : the individual distances of the original data points to their mean value :
39.7, 13.7, 11.7, 9.7, 7.7, 6.7, 2.7, 1.7, 0.3, 1.3, 2.3, 3.3, 4.3, 5.3, 9.3, 10.3, 12.3, 13.3, 15.3, 16.3
the man value for these is the MAD of the original data points :
187.2/20 = 9.36
=> B is correct
71.
the range is the difference between the highest and lowest values in a set of numbers.
so, in our case that is
98 - 42 = 56
=> AD is correct
72.
quartiles are the values that divide a list of numbers into quarters (4 equally long parts).
we have here 20 numbers, so all Qs are between 2 numbers.
Q1 is between the 5th and the 6th number (and again, the mean value between these two numbers is the result) :
Q1 = (74 + 75)/2 = 74.5
=> AE is correct
73.
as above, just for Q3 it is between the 15th and 16th number :
Q3 = (91 + 92)/2 = 91.5
=> DE is correct
74.
the interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.
while the range gives you the spread of the whole data set, the interquartile range gives you the range of the middle half of a data set - so, between Q1 and Q3 :
91.5 - 74.5 = 17
=> E is correct
75.
outliers are extreme values that differ from most other data points in a dataset (much lower or higher than the others).
outliers are therefore values at the extreme ends of a dataset.
often we see at least some of them right away, like 42 in our set.
but are there any others ?
there are some guidelines like building an upper and lower "fence" (or limit), and any value beyond these limits are great candidates for being outliers.
upper fence = Q3 + 1.5 × IQR = 91.5 + 1.5×17 = 117
we have no values higher than 117.
lower fence = Q1 - 1.5 × IQR = 74.5 - 1.5×17 = 49
we have one value (as expected) lower than that (42), which makes this a confirmed outlier.
=> AB is correct.