How to find mode - ISEE Upper Level Quantitative Reasoning

(a) The median of a data set with ten elements is the arithmetic mean of the fifth-highest and sixth-highest elements. These elements are 13 and 15, so the median is

(b) The mode of a data set is the element that occurs most frequently. Since 13 is the only repeated element, it is the mode.

This makes (a) the greater quantity.

The mode of a set of data is the value which occurs most frequently, which in this case is .

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So the mean of is greater than the mode.

The mode of a set of data is the value which occurs most frequently, which in this case is .

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So the mean is greater than the mode.

At current, 40 appears four times, more than any other value. For a set to be bimodal, it needs to have two modes; that is, another value would have to appear four times as well. Regardless of whether 30, 50, 60, or any other value replaces the box, this is impossible. The set cannot be made bimodal by adding one element.

The mode of a data set is the element that appears the most frequently. When two numbers both appear most frequently, there are two modes:

(a) The median of a data set with ten elements is the arithmetic mean of the fifth-highest and sixth-highest elements. These elements are 13 and 15, so the median is

(b) The mode of a data set is the element that occurs most frequently. Since 13 is the only repeated element, it is the mode.

This makes (a) the greater quantity.

The mode of a set of data is the value which occurs most frequently, which in this case is .

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So the mean of is greater than the mode.

The mode of a set of data is the value which occurs most frequently, which in this case is .

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So the mean is greater than the mode.

At current, 40 appears four times, more than any other value. For a set to be bimodal, it needs to have two modes; that is, another value would have to appear four times as well. Regardless of whether 30, 50, 60, or any other value replaces the box, this is impossible. The set cannot be made bimodal by adding one element.

The mode of a data set is the element that appears the most frequently. When two numbers both appear most frequently, there are two modes:

The mode of a data set is the element that appears most frequently.

The data set has ten elements - one 2, one 3, three 4's, two 7's, one 9, one 10, and an element of unknown value.

If that unknown element is 7, there are two modes of the set, 4 and 7, which would occur three times each, as opposed to the other elements, which would appear once each.

If that unknown element is any other integer, then the only mode of the data set is 4, which would occur three times, as opposed to the other elements, which would appear once or twice each.

The correct choice is that this impossible.

The mode of a data set is the element that appears most frequently.

Two values of the data set, 2 and 9, are known to appear twice; the others appear exactly once.

If is 6, 7, or 8, this does not change, and 2 and 9 are both modes.

If is 1, 3, 4, 5, or 10, then three different values appear twice, and 2, 9, and the choice of are the three modes.

If is 2 or 9, then that number appears three times, the other number appears twice, and all others appear once. That makes the choice of the only mode.

This makes the correct choice 2 or 9.

The mode of a set of data is the value which occurs most frequently, which in this case is .

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So the mean of is greater than the mode.

The mode of a set of data is the value which occurs most frequently, which in this case is .

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So the mean is greater than the mode.

At current, 40 appears four times, more than any other value. For a set to be bimodal, it needs to have two modes; that is, another value would have to appear four times as well. Regardless of whether 30, 50, 60, or any other value replaces the box, this is impossible. The set cannot be made bimodal by adding one element.

The mode of a data set is the element that appears the most frequently. When two numbers both appear most frequently, there are two modes:

The mode of a data set is the element that appears most frequently.

Two values of the data set, 2 and 9, are known to appear twice; the others appear exactly once.

If is 6, 7, or 8, this does not change, and 2 and 9 are both modes.

If is 1, 3, 4, 5, or 10, then three different values appear twice, and 2, 9, and the choice of are the three modes.

If is 2 or 9, then that number appears three times, the other number appears twice, and all others appear once. That makes the choice of the only mode.

This makes the correct choice 2 or 9.

The mode of a set of data is the value which occurs most frequently, which in this case is .

The mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

So the mean of is greater than the mode.

The mode of a data set is the element that appears the most frequently. When two numbers both appear most frequently, there are two modes:

If a data set has an even number of values, the median is the average of the two middle values. First we should put the numbers in order:

So the median is:

The mode of a set of data is the value which occurs most frequently, which is in this problem. So the mode is greater than the median.