GMAT Quantitative › Calculating mode
Consider the data set . It is known that
. How many modes does this data set have, and what are they?
The set has one mode, 6.
The set has two modes, 6 and 8.
The set has two modes, 6 and .
The set has one mode, .
The set has three modes, 6, 8, and .
Of the known elements, 6 occurs the most frequently - three times. Since the unknown occurs only twice, and it cannot be equal to any of the other elements, its value does not affect the status of 6 as the most frequent element. Therefore, regardless of
, 6 is the only mode.
True or false: is the arithmetic mean of the set
.
Statement 1:
Statement 2: is the arithmetic mean of
and
.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
Assume both statements to be true, and examine two cases.
Case 1:
The arithmetic mean of and
is
The conditions of both statements are satisfied.
The mean of the five numbers is their sum divided by 5:
Case 2:
The arithmetic mean of and
is
The conditions of both statements are satisfied.
But the mean of the five numbers is
Therefore, the mean may or may not be equal to .
Rita keeps track of the number of times she goes to the gym each week for 1260 weeks. She goes 1 day a week for 119 weeks, 2 days a week for 254 weeks, 3 days a week for 376 weeks, and 4 days a week for 511 weeks. What is the mode of the number of days she goes to the gym each week?
4 days/week
511 weeks
1 day/week
119 weeks
2.5 days/week
The mode is the number that comes up most frequently in a set. Rita goes to the gym 4 times a week for 511 weeks. She clearly goes 4 times per week far more often than she goes 1, 2, or 3 times per week. Therefore the mode is 4 days/week. It is NOT 511 weeks. That is the frequency with which 4 days/week occurs, but not the mode.
Find the mode of the following set of numbers:
The mode is the most frequent number, thus the answer is .
Find the mode of the following set of numbers.
The mode is the most frequent number. Thus, our answer is .
What is the mode for the following set:
The mode is the number that appears most frequently:
Determine the mode of the following set of data:
The mode of a set of data is the entry that appears most often within the set. One easy way to determine the mode is by arranging the set in increasing order:
Now that the set is arranged in increasing order, we can see how often each value appears in the set. The value 7 appears three times, which is more than any other entry is repeated, so this is the mode of the set.
Determine the mode for the following set of numbers.
The mode is the most frequent number, thus our answer is .
Give the mode of the set .
The set has no mode.
The mode of a set, if it exists, is the value that occurs most frequently. The inequality
means that the set
can be rewritten as
.
The most frequently occurring value is , making this the mode.
.
Give the mode of the set .
The mode of a set, if it exists, is the value that occurs most frequently. The inequality
means that the set
can be rewritten as
and
occur as values twice each; the other values,
and
, are unique. Therefore, the set has two modes,
and
.