Basic Statistics

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Questions 11 - 20
11

What is the mode?

Explanation

Mode is the data point that occurs most frequently.

Let's arrange in increasing order. We have

.

and occur twice and are the most frequent. We can have more than one mode so the answer is .

12

What is the mode?

Explanation

Mode is the data point that occurs most frequently.

Let's arrange in increasing order. We have

.

and occur twice and are the most frequent. We can have more than one mode so the answer is .

13

A P.E. class took the height of every student in inches. These were the results:

Find the median of the class's data set.

Explanation

Median means the middle of a sorted set of numbers. That is, it is the exact middle of a set of numbers.

In order to solve for median, we must allign the numbers in order in increasing value.

This number set will become:

As you cross out one number from each side, you will eventually be left with the remaining number if there is an odd number of numbers. If there is an even number of numbers, the median will be the average of the last two remaining numbers.

Because we're left with two numbers, we must take their mean (average) to solve for the median of the data set.

14

A P.E. class took the height of every student in inches. These were the results:

Find the median of the class's data set.

Explanation

Median means the middle of a sorted set of numbers. That is, it is the exact middle of a set of numbers.

In order to solve for median, we must allign the numbers in order in increasing value.

This number set will become:

As you cross out one number from each side, you will eventually be left with the remaining number if there is an odd number of numbers. If there is an even number of numbers, the median will be the average of the last two remaining numbers.

Because we're left with two numbers, we must take their mean (average) to solve for the median of the data set.

15

What is the mode?

Explanation

Mode is the data point that occurs most frequently.

Let's arrange in increasing order. We have

.

occur twice while the rest only once.

Therefore, is our final answer.

16

Consider the following set of numbers:

Find the mode of the set.

Explanation

The mode of the set is the most repeated number in the set. In this case there is number being repeated once and another being repeated twice.

Therefore the answer will be the number that is being repeated twice, .

This number can be seen in red.

17

What is the mode?

Explanation

Mode is the data point that occurs most frequently.

Let's arrange in increasing order. We have

.

occur twice while the rest only once.

Therefore, is our final answer.

18

Consider the following set of numbers:

Find the mode of the set.

Explanation

The mode of the set is the most repeated number in the set. In this case there is number being repeated once and another being repeated twice.

Therefore the answer will be the number that is being repeated twice, .

This number can be seen in red.

19

Using the data above, find the median.

Explanation

The median is the numer that, when put in numerical order, appears in the direct center of the group.

To find this value, we must first put the numbers in numerical order:

.

In this set of data we have seven pieces of data, we subtract one, then divide the result in half,

.

This means that there must be three numbers on either side of the median.

To satisfy this requirement, our median must be .

20

What is the median of the following numbers?

12,15,93,32,108,22,16,21

Explanation

To find the median, first you arrange the numbers in order from least to greatest.

Then you count how many numbers you have and divide that number by two. In this case 12,15,16,21,22,32,93,108= 8 numbers.

So

Then starting from the least side of the numbers count 4 numbers till you reach the median number of

Then starting from the greatest side count 4 numbers until you reach the other median number of

Finally find the mean of the two numbers by adding them together and dividing them by two

to find the median number of .

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