Calculating the mean, the median, and the mode when scores are changed are or re
ID: 3255821 • Letter: C
Question
Calculating the mean, the median, and the mode when scores are changed are or removed Consider the following sample set of scores. Assume these scores are from a discrete distribution. For the given data, the mean is ______, the median is ______, and the mode is ______. Suppose the score 2 in the data is mistakenly recorded as 28 instead of 2. For the sample with the error, the mean is ______, the median is ______, and the mode is ______. The mean ______, the median _____, and the mode ______. Suppose the score 2 in the original sample is inadvertently removed from the sample. For the sample with this score removed, the mean is ______, the median is ______, and the mode is ______. The mean ______, the median ______, and the mode ______.Explanation / Answer
a) 2,30,32,38,38,45,50,64,72,100
mean = sum of all terms / number of all terms = 471 /10 = 47.1
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
2 30 32 38 38 45 50 64 72 100
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median=(38+45)/2=41.5
mode
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
2 30 32 38 38 45 50 64 72 100
We see that the mode is 38 .
b) 28,30,32,38,38,45,50,64,72,100
mean = 497/10 = 49.7
Ordering the data from least to greatest, we get:
28 30 32 38 38 45 50 64 72 100
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median=(38+45)/2=41.5
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
28 30 32 38 38 45 50 64 72 100
We see that the mode is 38 .
c)
mean = 469/9
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
30 32 38 38 45 50 64 72 100
So, the median is 45 .
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
30 32 38 38 45 50 64 72 100
We see that the mode is 38 .
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