Data Analysis, Probability, and Statistics - HiSET
Card 1 of 136
Consider the following data set:
Which of the following gives the arithmetic mean of the set in terms of 
?
Consider the following data set:
Which of the following gives the arithmetic mean of the set in terms of 
Tap to reveal answer
The arithmetic mean of a data set is the sum of the items in the set divided by the number of items. There are ten items, so the mean is
Simplify the numerator by combining the like terms:
Now, split the fraction, and reduce to lowest terms:
,
the correct response.
The arithmetic mean of a data set is the sum of the items in the set divided by the number of items. There are ten items, so the mean is
Simplify the numerator by combining the like terms:
Now, split the fraction, and reduce to lowest terms:
the correct response.
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Consider the data set
,
where 
is a prime integer.
How many possible values of 
make the set bimodal?
Consider the data set
where 
How many possible values of 
Tap to reveal answer
The mode of a data set is the value that occurs most frequently in the set. If two values tie for most frequently occurring value, then the set has two modes - it is bimodal.
The value 29 already occurs three times in the data set. For the set to be bimodal, 
must be equal to one of the values that occurs once - 17, 21, 27, 35, or 37. Since it is given that 
is prime - having only two factors, 1 and itself - 
can only be either of 17 and 37, the other three values having other factors.
The correct response is two.
The mode of a data set is the value that occurs most frequently in the set. If two values tie for most frequently occurring value, then the set has two modes - it is bimodal.
The value 29 already occurs three times in the data set. For the set to be bimodal, 
The correct response is two.
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Consider the following data set:
where 
is an integer from 1 to 10 inclusive.
How many possible values of 
make 8 the median of the set?
Consider the following data set:
where 
How many possible values of 
Tap to reveal answer
The median of a set of nine data values - an odd number - is the value that appears in the middle when the values are ranked. For 8 to be the median, 8 must be in the middle - that is, four values must appear before 8, and four values must appear after 8.
In the given data set, four values - 4, 5, 5, 6 - are known to be appear before 8, so 
must appear after 8. Since 
is an integer from 1 to 10, 
can only be 8, 9, or 10. This makes three the correct response.
The median of a set of nine data values - an odd number - is the value that appears in the middle when the values are ranked. For 8 to be the median, 8 must be in the middle - that is, four values must appear before 8, and four values must appear after 8.
In the given data set, four values - 4, 5, 5, 6 - are known to be appear before 8, so 
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Consider the data set
,
where is a prime integer.
How many possible values of make the set bimodal?
Consider the data set
where
How many possible values of
Tap to reveal answer
The mode of a data set is the value that occurs most frequently in the set. If two values tie for most frequently occurring value, then the set has two modes - it is bimodal.
The value 29 already occurs three times in the data set. For the set to be bimodal, must be equal to one of the values that occurs once - 17, 21, 27, 35, or 37. Since it is given that is prime - having only two factors, 1 and itself - can only be either of 17 and 37, the other three values having other factors.
The correct response is two.
The mode of a data set is the value that occurs most frequently in the set. If two values tie for most frequently occurring value, then the set has two modes - it is bimodal.
The value 29 already occurs three times in the data set. For the set to be bimodal,
The correct response is two.
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Consider the following data set:
where is an integer from 1 to 10 inclusive.
How many possible values of make 8 the median of the set?
Consider the following data set:
where
How many possible values of
Tap to reveal answer
The median of a set of nine data values - an odd number - is the value that appears in the middle when the values are ranked. For 8 to be the median, 8 must be in the middle - that is, four values must appear before 8, and four values must appear after 8.
In the given data set, four values - 4, 5, 5, 6 - are known to be appear before 8, so must appear after 8. Since is an integer from 1 to 10, can only be 8, 9, or 10. This makes three the correct response.
The median of a set of nine data values - an odd number - is the value that appears in the middle when the values are ranked. For 8 to be the median, 8 must be in the middle - that is, four values must appear before 8, and four values must appear after 8.
In the given data set, four values - 4, 5, 5, 6 - are known to be appear before 8, so
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Consider the data set
,
where is a prime integer.
How many possible values of make the set bimodal?
Consider the data set
where
How many possible values of
Tap to reveal answer
The mode of a data set is the value that occurs most frequently in the set. If two values tie for most frequently occurring value, then the set has two modes - it is bimodal.
The value 29 already occurs three times in the data set. For the set to be bimodal, must be equal to one of the values that occurs once - 17, 21, 27, 35, or 37. Since it is given that is prime - having only two factors, 1 and itself - can only be either of 17 and 37, the other three values having other factors.
The correct response is two.
The mode of a data set is the value that occurs most frequently in the set. If two values tie for most frequently occurring value, then the set has two modes - it is bimodal.
The value 29 already occurs three times in the data set. For the set to be bimodal,
The correct response is two.
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Consider the following data set:
where is an integer from 1 to 10 inclusive.
How many possible values of make 8 the median of the set?
Consider the following data set:
where
How many possible values of
Tap to reveal answer
The median of a set of nine data values - an odd number - is the value that appears in the middle when the values are ranked. For 8 to be the median, 8 must be in the middle - that is, four values must appear before 8, and four values must appear after 8.
In the given data set, four values - 4, 5, 5, 6 - are known to be appear before 8, so must appear after 8. Since is an integer from 1 to 10, can only be 8, 9, or 10. This makes three the correct response.
The median of a set of nine data values - an odd number - is the value that appears in the middle when the values are ranked. For 8 to be the median, 8 must be in the middle - that is, four values must appear before 8, and four values must appear after 8.
In the given data set, four values - 4, 5, 5, 6 - are known to be appear before 8, so
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Which of the following is an example of a set with no mode?
Which of the following is an example of a set with no mode?
Tap to reveal answer
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given, 
is the only one that fits this definition.
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given, 
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Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which is the least?
Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which is the least?
Tap to reveal answer
The mean of a data set 
is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
.
Of the four - mean, median, mode, and midrange - the median and the mode tie for being the least.
The mean of a data set
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
Of the four - mean, median, mode, and midrange - the median and the mode tie for being the least.
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Which of the following is an example of a set with no mode?
Which of the following is an example of a set with no mode?
Tap to reveal answer
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given, is the only one that fits this definition.
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given,
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Which of the following is an example of a set with no mode?
Which of the following is an example of a set with no mode?
Tap to reveal answer
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given, is the only one that fits this definition.
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given,
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Which of the following is an example of a set with no mode?
Which of the following is an example of a set with no mode?
Tap to reveal answer
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given, is the only one that fits this definition.
The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given,
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Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which two are equal?
Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which two are equal?
Tap to reveal answer
The mean of a data set 
is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
.
Of the four - mean, median, mode, and midrange - the median and the mode are equal.
The mean of a data set 
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
Of the four - mean, median, mode, and midrange - the median and the mode are equal.
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Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which is the least?
Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which is the least?
Tap to reveal answer
The mean of a data set is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
.
Of the four - mean, median, mode, and midrange - the median and the mode tie for being the least.
The mean of a data set
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
Of the four - mean, median, mode, and midrange - the median and the mode tie for being the least.
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Consider the following data set:
If 
, which is true of the mode or modes of the data set?
Consider the following data set:
If 
Tap to reveal answer
The mode of a data set is the value that occurs most frequently in the set. If two or more values tie for most frequently occurring value, then the set has multiple modes.
We show that the question of the modes of the data set cannot be answered with certainty as follows:
Suppose 
assumes a value in the data set - for example, let 
. the data set is
,
in which the most frequently occurring value is 1, which appears . This makes 1, 
, the mode.
Now, suppose 
assumes a value not already in the data set; for example, let 
. The data set becomes
,
in which two values, 2 (the 
) and 8 each occur twice.
Therefore, from the information given, the mode(s) cannot be determined with any certainty.
The mode of a data set is the value that occurs most frequently in the set. If two or more values tie for most frequently occurring value, then the set has multiple modes.
We show that the question of the modes of the data set cannot be answered with certainty as follows:
Suppose 
in which the most frequently occurring value is 1, which appears . This makes 1, 
Now, suppose 
in which two values, 2 (the 
Therefore, from the information given, the mode(s) cannot be determined with any certainty.
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Consider the following data set:
where 
is an integer from 1 to 10 inclusive.
How many possible values of 
make 5 the median of the set?
Consider the following data set:
where 
How many possible values of 
Tap to reveal answer
The median of a set of eleven data values - an odd number - is the value that appears in the middle when the values are ranked. For 5 to be the median, 5 must be in the middle - that is, five values must appear before 5, and five values must appear after 8.
We can answer this question by looking at three cases.
Case 1: 
Without loss of generality, assume 
; this reasoning holds for any lesser value of 
. The data set becomes
,
and the median is 4.
Case 2: 
The data set becomes
The middle value - the median - is 5.
Case 3: 
Without loss of generality, assume 
; this reasoning holds for any greater value of 
. The data set becomes
Again, the median is 5.
Therefore, we can set 
equal to 5, 6, 7, 8, 9, or 10 - any of six different values - and make the median of the set 5.
The median of a set of eleven data values - an odd number - is the value that appears in the middle when the values are ranked. For 5 to be the median, 5 must be in the middle - that is, five values must appear before 5, and five values must appear after 8.
We can answer this question by looking at three cases.
Case 1:
Without loss of generality, assume 
and the median is 4.
Case 2:
The data set becomes
The middle value - the median - is 5.
Case 3:
Without loss of generality, assume 
Again, the median is 5.
Therefore, we can set 
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Consider the data set:
Which is true of the arithmetic mean 
, the median 
, and the midrange 
?
Consider the data set:
Which is true of the arithmetic mean 
Tap to reveal answer
The mean of a data set is equal to the sum of the entries divided by the number of entries. There are nine entries in the set, so
The median of a data set with an odd number of values is the value of the entry in the middle when the values are arranged in ascending order:
This value is 
.
The midrange of a data set is the arithmetic mean of the least and greatest elements in the set. This element is
The correct response is that
.
The mean of a data set is equal to the sum of the entries divided by the number of entries. There are nine entries in the set, so
The median of a data set with an odd number of values is the value of the entry in the middle when the values are arranged in ascending order:
This value is 
The midrange of a data set is the arithmetic mean of the least and greatest elements in the set. This element is
The correct response is that
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Consider the following data set:
where 
is an integer from 1 to 10 inclusive.
How many possible values of 
make 
the median of the set?
Consider the following data set:
where 
How many possible values of 
Tap to reveal answer
The median of a set of ten data values - and even number - is the arithmetic mean of the two values that appear in the middle when the values are ranked. For 
to be the median, it would have to hold that either the two middle values are both 
. The data set, in ascending order, would be as follows:
.
must be between 6 and 8 inclusive. Since it is given that 
is an integer, there are three possibilities: 6, 7, and 8.
Three is the correct response.
The median of a set of ten data values - and even number - is the arithmetic mean of the two values that appear in the middle when the values are ranked. For 
Three is the correct response.
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Consider the data set:
Which is true of the arithmetic mean 
, the median 
, and the midrange 
?
Consider the data set:
Which is true of the arithmetic mean 
Tap to reveal answer
The mean of a data set is equal to the sum of the entries divided by the number of entries. There are ten entries in the set, so
The median of a data set with an even number of values is the arithmetic mean of the values of the two entries in the middle when the values are arranged in ascending order:
This value is 
.
The midrange of a data set is the arithmetic mean of the least and greatest elements in the set. This element is
The correct response is that
.
The mean of a data set is equal to the sum of the entries divided by the number of entries. There are ten entries in the set, so
The median of a data set with an even number of values is the arithmetic mean of the values of the two entries in the middle when the values are arranged in ascending order:
This value is 
The midrange of a data set is the arithmetic mean of the least and greatest elements in the set. This element is
The correct response is that
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Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which two are equal?
Consider the data set
Of the mean, the median, the mode, and the midrange of the data set, which two are equal?
Tap to reveal answer
The mean of a data set is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
.
Of the four - mean, median, mode, and midrange - the median and the mode are equal.
The mean of a data set
The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:
so the element that falls in the middle is 12.
The mode of the data set is the term that occurs most frequently, which is 12.
The midrange is the mean of the least and greatest elements, which is
Of the four - mean, median, mode, and midrange - the median and the mode are equal.
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