What do you call the middle number in a data set when arranged either in ascending?

2 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 3 What do you call the number that occurs most often in a data set? A median B. mode C. range D. mean

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Gauthmathier0341

Grade 9 · 2021-06-06

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2) 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 3) What do you call the number that occurs most often in a data set?
A median
B. mode
C. range
D. mean

Stella

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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.

What Is the Median?

The median is the middle number in a sorted, ascending or descending list of numbers and can be more descriptive of that data set than the average. It is the point above and below which half (50%) the observed data falls, and so represents the midpoint of the data.

The median is often compared with other descriptive statistics such as the mean (average), mode, and standard deviation.

Key Takeaways

• The median is the middle number in a sorted list of numbers and can be more descriptive of that data set than the average.
• The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
• If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
• If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.
• In a normal distribution, the median is the same as the mean and the mode.

Understanding the Median

Median is the middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest. The median can be used to determine an approximate average, or mean, but is not to be confused with the actual mean.

• If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
• If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.
  

The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values. The median of a sequence can be less affected by outliers than the mean.

Median Example

To find the median value in a list with an odd amount of numbers, one would find the number that is in the middle with an equal amount of numbers on either side of the median. To find the median, first arrange the numbers in order, usually from lowest to highest.

For example, in a data set of {3, 13, 2, 34, 11, 26, 47}, the sorted order becomes {2, 3, 11, 13, 26, 34, 47}. The median is the number in the middle {2, 3, 11, 13, 26, 34, 47}, which in this instance is 13 since there are three numbers on either side.

To find the median value in a list with an even amount of numbers, one must determine the middle pair, add them, and divide by two. Again, arrange the numbers in order from lowest to highest.

For example, in a data set of {3, 13, 2, 34, 11, 17, 27, 47}, the sorted order becomes {2, 3, 11, 13, 17, 27, 34, 47}. The median is the average of the two numbers in the middle {2, 3, 11, 13, 17,2634, 47}, which in this case is fifteen {(13 + 17) ÷ 2 = 15}.

The median is closely associated with quartiles, or dividing up observed data into four equal parts. The median would be the center point, with the first two quartiles falling below it and the second two above it. Other ways of bucketing data include quintiles (in five sections) and deciles (in 10 sections).

How Do You Calculate the Median?

The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median. If the number of observations is even, take the average of the values found above and below that position.

Where Is the Median in a Normal Distribution?

In the normal distribution ("bell curve") the median, mean, and mode are all the same value, and fall at the highest point in the center of the curve.

When Is the Mean and Median Different?

In a skewed data set, the mean and median will typically be different. The mean is calculated by adding up all of the values in the data and dividing by the number of observations. If there are sizable outliers, or if the data clumps around certain values, the mean (average) will not be the midpoint of the data.

For instance, in a set of data {0, 0, 0, 1, 1, 2, 10, 10} the average would be 24/8 = 3. The median, however, would be 1 (the midpoint value).

This is why many economists favor the median for reporting a nation's income or wealth, since it is more representative of the actual income distribution.

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