How to find mode

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ISEE Upper Level Quantitative Reasoning › How to find mode

Questions 1 - 10

What is the mode value in the set below?

$2^{2}, \frac{1}{4}, 3^{1},\sqrt{9}, \frac{8}{2}, \frac{6}{2}$

Explanation

The first step is to convert the expressions in the set $2^{2}, \frac{1}{4}, 3^{1},\sqrt{9}, \frac{8}{2}, \frac{6}{2}$ to their simplified forms. This gives us:

$4, \frac{1}{4}, 3, 3, 4, 3$

While the value of 4 appears twice, given that the value 3 appears 3 times, it is the mode in this set.

Give the mode(s) of the data set:

$\left { 1, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10\right }$

$4,5,\textrm{ and }7$

$5 \frac{1}{3}$

The data set has no mode.

Explanation

The mode of a data set is the element that appears most frequently. In this set, that element is , which appears three times. No other element appears more than twice.

Find the mode of the following data set:

Explanation

Find the mode of the following data set:

First, let's put our terms in increasing order:

Now, our mode will just be our most common term. In this case it is 33.

In the following set of scores find the mode:

$\begin{matrix} Data \ Value & Frequency \ 80& 12\ 74& 14\ 85& 7\ 82& 8\ 64& 11 \end{matrix}$

Explanation

The mode is the value that appears most often or has more frequency in a given set of data. So in this problem, the mode is which occurs most frequently.

Find the mode and the median of the frequency distribution shown in the following table:

$\begin{matrix} Data \ Value & Frequency \ 77 & 7\ 79& 3\ 82& 4\ 88& 1 \end{matrix}$

$Mode=77\ , Median=79$

$Mode=77\ , Median=78$

$Mode=78\ , Median=79$

$Mode=78\ , Median=80$

$Mode=82\ , Median=79$

Explanation

The mode is the value that appears most often or has more frequency which is in this problem. The total number of data values are . Since the number of values is odd, the median is the single middle value which is the value in this problem. So the median is .

Use the following data set of test scores to answer the question:

Find the mode.

Explanation

To find the mode of a data set, we will find the number the appears most often.

So, given the set

We can see the number that appears most often is 99.

Therefore, the mode of the data set is 99.

A data set has six known quantities and one unknown quantity, as follows:

$\left { 15, 25, 25, 35, 35, 40, N \right }$

Which is the greater quantity?

(A) The mode of the set if

(b) The mode of the set if

(A) is greater

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

Explanation

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

If , the set becomes $\left { 15, 25, 25, 35, 35, 35, 40 \right }$ .

The mode is 35, which occurs three times, more than any other element.

If , the set becomes $\left { 15, 25, 25, 25, 35, 35, 40 \right }$ .

The mode is 25, which occurs three times, more than any other element.

(A) is greater.

Compare the median and the mode in the following set of data:

$\left { 0,0.1,0.1,0.01,0.01,0.01,0.001 \right }$

The median and the mode are equal.

The median is greater than the mode.

The mode is greater than the median.

It is not possible to compare the mode and the median based on the information given.

Explanation

If there are an odd number of values in a data set, the median is the middle value. In this problem first we should put the numbers in order:

$\left { 0,0.001,0.01,0.01,0.01,0.1,0.1 \right }$

So the median is .

The mode of a set of data is the value which occurs most frequently, which is . So the median and the mode are equal.

Consider the data set

$\left { 5, 8, 9, 12, 5, 7, 10, 5, N \right }$ ,

where is unknown.

Which is the greater quantity?

(a) The mode of the data set

(b) 5

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

Explanation

5 appears in the data set at least three times. Regardless of the value of , no other element (except 5) can appear more than twice. 5 must be the mode.

Compare the mean and the mode in the following set of data:

$\left { \frac{1}{2},\frac{2}{3},\frac{3}{4},\frac{5}{6},\frac{1}{2} \right }$

The mean is greater than the mode.

The mode is greater than the mean.

The mean and the mode are equal.

It is not possible to compare the mean and the mode based on the information given.

Explanation

The mode of a set of data is the value which occurs most frequently, which in this case is $\frac{1}{2}=0.5$ .

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:

$Mean = \frac{\frac{1}{2}+\frac{2}{3}+\frac{3}{4}+\frac{5}{6}+\frac{1}{2}}{5}=\frac{\frac{6+8+9+10+6}{12}}{5}=\frac{39}{60}=\frac{13}{20}=0.65$

So the mean is greater than the mode.

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