Is the middle value in the distribution when it is arranged in descending or ascending order Mcq?

The Mean of a Data Set

The mean of a set of numbers, sometimes simply called the average , is the sum of the data divided by the total number of data.

Example 1 :

Find the mean of the set { 2 , 5 , 5 , 6 , 8 , 8 , 9 , 11 } .

There are 8 numbers in the set. Add them all, and then divide by 8 .

2 + 5 + 5 + 6 + 8 + 8 + 9 + 11 8 = 54 8 = 6.75

So, the mean is 6.75 .

The Median of a Data Set

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

Example 1 :

Find the median of the set { 2 , 5 , 8 , 11 , 16 , 21 , 30 } .

There are 7 numbers in the set, and they are arranged in ascending order.  The middle number (the 4 th one in the list) is 11 .  So, the median is 11 .

Example 2 :

Find the median of the set { 3 , 10 , 36 , 255 , 79 , 24 , 5 , 8 } .

First, arrange the numbers in ascending order.

{ 3 , 5 , 8 , 10 , 24 , 36 , 79 , 255 }

There are 8 numbers in the set -- an even number. So, find the average of the middle two numbers, 10 and 24 .

10 + 24 2 = 34 2 = 17

So, the median is 17 .

The Mode of a Data Set

The mode of a set of numbers is the number which occurs most often.

Example 1 :

Find the mode of the set { 2 , 3 , 5 , 5 , 7 , 9 , 9 , 9 , 10 , 12 } .

2 , 3 , 7 , 10 and 12 each occur once.

5 occurs twice and 9 occurs three times.

So, 9 is the mode.

Example 2 :

Find the mode of the set { 2 , 5 , 5 , 6 , 8 , 8 , 9 , 11 } .

In this case, there are two modes -- 5 and 8 both occur twice, whereas the other numbers only occur once.

Mean, Median, Mode, and Range

• 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

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

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?

Solution 

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

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.

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Guided Practice (Ask your tutor for help.)

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

Is the middle value when the data are arranged in ascending or descending rank order?

What is the middle value when a variables are ranked in order is called?

Can median be in descending order?

Is the middle number in a set of data when arranged in decreasing order?