Median

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ISEE Upper Level Quantitative Reasoning › Median

Questions 1 - 10
1

Find the median of the following data set:

Explanation

Find the median of the following data set:

To find the median, first put the numbers in increasing order

Now, identify the median by choosing the middle term

In this case, it is 44, because 44 is in the middle of all our terms.

2

Find the median of the following data set:

Explanation

Find the median of the following data set:

To find the median, first put the numbers in increasing order

Now, identify the median by choosing the middle term

In this case, it is 44, because 44 is in the middle of all our terms.

3

Use the following data set to answer the question:

Find the median.

Explanation

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will locate the number in the center of the data set.

So, given the data set

we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get

Now, we will locate the number in the center of the data set.

We can see that it is 6.

Therefore, the median of the data set is 6.

4

Use the following data set to answer the question:

Find the median.

Explanation

To find the median of a data set, we will first arrange the numbers in ascending order. Then, we will locate the number in the center of the data set.

So, given the data set

we will arrange the numbers in ascending order. To do that, we will arrange them from smallest to largest. So, we get

Now, we will locate the number in the center of the data set.

We can see that it is 6.

Therefore, the median of the data set is 6.

5

Which is the greater quantity?

(a) The mean of the first ten prime numbers

(b) The median of the first ten prime numbers

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Explanation

The first ten primes form the data set:

(a) Add these primes, and divide by :

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

.

(a) is the greater quantity.

6

Which is the greater quantity?

(a) The mean of the first ten prime numbers

(b) The median of the first ten prime numbers

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Explanation

The first ten primes form the data set:

(a) Add these primes, and divide by :

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

.

(a) is the greater quantity.

7

Consider the data set

.

For what value(s) of would this set have median ?

Any number greater than or equal to

Any number greater than

Any number less than or equal to

Any number less than

Any number except

Explanation

Arrange the eight known values from least to greatest.

For to be the median of the nine elements, it muct be the fifth-greatest, This happens if .

8

Consider the data set

.

For what value(s) of would this set have median ?

Any number greater than or equal to

Any number greater than

Any number less than or equal to

Any number less than

Any number except

Explanation

Arrange the eight known values from least to greatest.

For to be the median of the nine elements, it muct be the fifth-greatest, This happens if .

9

If is a real number, find the median in the following set of data in terms of .

Explanation

The data should first be ordered:

When the number of values is even, the median is the mean of the two middle values. So in this problem we need to find the mean of the and values:

10

If is a real number, find the median in the following set of data in terms of .

Explanation

The data should first be ordered:

When the number of values is even, the median is the mean of the two middle values. So in this problem we need to find the mean of the and values:

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