What do you call the middle number in a data set when the numbers are arranged in descending order?

What do you call the middle number in a data set when the numbers are arranged in descending order?

You may have heard the terms descending and ascending order before, but what do they actually mean?

This article explains in plain English the basic differences between those two terms and gives an analogy that may help you distinguish one from the other.

When a series of data is arranged from high to low or largest to smallest, it means it is arranged is descending order, also known as decreasing order.

This could apply to any group of information such as numbers, dates, sizes of objects, or letters – the same principles apply to whatever you're dealing with.

For example, ordering a set of numbers from greatest to smallest value means that you're arranging them in descending order.

Say you have the following numbers: 49, 80, 56, 11, 20.

Sorting them in descending order would look like this: 80, 56, 49, 20, 11.

You always start first with the largest number on the left and end with the smallest one on the right. In this example, 80 is the largest and 11 is the smallest. The numbers in between are also in order from largest to smallest.

The numbers keep on decreasing, with each number being smaller than the previous number in the line.

The same goes for the letters of the alphabet. When arranging them in descending order, you'd write them out from Z to A (so, backwards). Think of this one from end to beginning.

The same goes for dates when you're putting things in chronological order – they're arranged from the latest and most recent one to the oldest one.

Think of it like going down (or descending) a set of stairs - when you do so you start from a high place and end up at a lower one. You start up at the top and want to go down.

What do you call the middle number in a data set when the numbers are arranged in descending order?

So, in a nutshell, descending order is the arrangement of items from highest to lowest.

What is ascending order?

Ascending order is the complete opposite of descending order - it is also known as increasing order of importance.

Items are arranged from lowest to highest value. The order starts with the smallest value coming first and ends with the biggest value.

So, taking the numbers from the previous section :49, 80, 56, 11, 20, and arranging them in ascending order would look like this: 11, 20, 49, 56, 80.

The smallest number always comes first, in this case it's 11, and the last one is always the greatest one, which is 80 in the example above.

Same rules apply for the letters of the alphabet. When arranging them in ascending order they are arranged from A to Z – or beginning to end.

When it comes to dates, ascending order would mean that the oldest ones come first and the most recent ones last.

Think of the staircase example again.

When you go up (or ascend) a set of stairs, you start from somewhere low and you end up at place much higher than the one you began with.

What do you call the middle number in a data set when the numbers are arranged in descending order?

In summary, ascending order is the arrangement of items from lowest to highest.

Thanks for reading!



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Mean, Median, Mode, and Range


Three types of averages can be used to describe a data set.

Averages

  • The mean of a data set is the sum of the values divided by the number of values.

  • The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values.

  • The mode of a data set is the value that occurs most often. A data set can have no mode, one mode, or more than one mode.
  • The range of a data set is the difference between the largest and smallest values in the set.


Math In Real Life 

Example

What do you call the middle number in a data set when the numbers are arranged in descending order?

A marine biologist records the locations of deep sea jellies in relation to the ocean surface. Jellies are found at -2,278 feet, -1,875 feet, -3,210 feet, -2,755 feet, -2,407 feet, and -2,901 feet. 

What is the average location of a deep sea jelly?


Find the Mean

To find the mean of the 6 locations of the deep sea jellies in the problem above, divide the sum of the locations by 6. 

The mean location in relation to the ocean surface is -2571 ft.


Guided Practice (Ask your tutor for help.) 


1) Find the mean of the data. 


2) Find the mean of the data.
  


Finding Median, Mode, and Range


Find the median, mode(s), and range of the movie prices below.

$7.20, $13.25, $14.94, $16.56, $18.74, $19.99, $19.99, $29.49

Median

The data set has an even number of prices, so the median is the mean of the two middle values, $16.56 and $18.74. 


Mode

The price that occurs most often is $19.99. This is the mode. 


Range


The range of a data set is the difference of the greatest value and the least value.

Range = $29.49-$7.20=$22.29


Choosing a Representative Average

Groups A and B try a new ice cream flavor and rate it on a scale of 1 to 10 as shown. Which average best represents each group?

What do you call the middle number in a data set when the numbers are arranged in descending order?
 


Solution 

What do you call the middle number in a data set when the numbers are arranged in descending order?

The mean, median, and mode are very close. So each average is a fair representation of the ratings as a group. 

What do you call the middle number in a data set when the numbers are arranged in descending order?

The mean is higher than all but 3 ratings. The mode is equal to the lowest rating. So, mean and mode are not good choices. The median best represents the ratings.


Guided Practice (Ask your tutor for help.)

3) Find the Error 
Describe and correct the error in the solution. 

What do you call the middle number in a data set when the numbers are arranged in descending order?



4) Use the data set 6, 12, 4, 15, 10, 6, 2, 9 to complete the statement using mean, median, mode, or range

a. The _?_ is 8.

b. The _?_ is 6.

c. The _?_ is 13.



5) Jocelyn is training to run in a race. Her practice times (in minutes and seconds) are 22:45, 21:56, 21:03, 20:33, and 20:28. 

Find her mean time to complete the race.

Step 1 Change Jocelyn's practice times to seconds.

Step 2 Find the sum of the practice times. Divide by the number of times.

Step 3 Convert your answer to minutes and seconds.

Answer Key

1)  16

1/8 in

2)  3.6oC

3)  The numbers 5 and 8 both appear three times, so there are two modes in the data set.

4)
a.  mean
b.  mode
c.  range

5)  21:21

What is the middle number when the data set is arranged in order?

The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values.

What do you call the middle number in a data set when arranged either in ascending or descending order a range B mean C median D mode?

The median is the middle value in distribution when the values are arranged in ascending or descending order.

What is it called when the data is arranged in ascending or descending order the middle value in set of observations?

The middle most observation, after arranging all observations in ascending or descending order, is called the median.

What is the middle of a data set called?

The "center" of a data set is also a way of describing location. The two most widely used measures of the "center" of the data are the mean (average) and the median.