The data set is in chronological order.  The median is 16.

The third quartile represents the median of the numbers that are above the known median.

Breaking the set into two

To find the third quartile we will take the median of the second cluster of numbers.

Therefore the third quartile is 23.

The third quartile, by definition, means that 75% of the data is below the data point. That means 25% is above (100%-75%).

The stem-and-leaf display represents 53 scores. The "stems" (or left column) represent the tens digits, and the "leaves" in each row represent units digits, so the scores are

The student who scored an 86 outscored 42 of the students, or

of them. Since percentile is given to the nearest whole number, the correct response is 79.

{95, 88, 70, 75, 83, 70, 66, 91, 68, 76, 82}

Arrange the values in numerical order.

{66, 68, 70, 70, 75, 76, 82, 83, 88, 91, 95}

Use the following to calculate percentile-

where  is the percentile and  is the number of data in the set

This number gives of the location of the 85th percentile in our ordered set. Since it is not a whole number, round up, which will give us 10.

The 85th percentile score is the 10th value in our set, which is 91.

The formula to calculate a percentile rank is:  

where  represents total of scores below the rank, and  is the total number of competitors.

Substitute the values into the formula.

First arrange the runners in order of fastest to slowest times:

Ron

Sarah

Jareth

Sean

Ankur

Fred 

There are six runners so there will be six different percentiles, each seperated by  percent. A person's percentile refers to which percentage of times are below that person's time. For example, Ron's time is better than  percent of all runners, so he is in the rd percentile.

Then each runner is in the following percentiles:

Ron - rd

Sarah - th

Jareth - th

Sean - rd

Ankur - th

Fred - th

As you can see, Sean is in the rd percentile.

The percentile is equal to how many items in the set are equal to or less than the one in question divided by the total number of items in the set.

Because there are four items equal to or less than the orange kitten's weight and there are nine items total in the set, the percentile is equal to

     or    

In the data set, 102 is the 6th data point listed. There are 14 data points total. This means that % of the data is at or below 102. That's approximately the 43rd percentile.

The number 110 is the 12th in the list of 14 data points. That means that %. Since about 86% of the data points are at or below 110, it's in the 86th percentile.

The stem-and-leaf display represents 53 scores. The score at the 35th percentile would be the score that is greater than 35% of the scores, or 

 scores.

Rounding, we count 19 scores from the bottom:

The score represented is 64, which is the correct response.