# How do I find the mean, median, mode, and midrange of the following sample: 1,2,4,7,8,9,10,20?

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Given the data set 1,2,4,7,8,9,10,20:

(1) The mean (arithmetic mean) is the sum of the data divided by the number, n, of pieces of data.

` bar(x)=(1+2+4+7+8+9+10+20)/8=61/8=7.625 `

Usually you report the mean to one more digit than the given data so `bar(x)=7.6 `

(2) The median is the number in the middle of the **ordered** data set. I.e. there are as many data points below the median as above the median.

Here the median is between 7 and 8; in the case that there is an even number of data points you take the mean of the two in the middle.

`"med"=(7+8)/2=7.5 `

(3) The mode is the datum that occurs the most often. A set can have no mode, 1 mode, or multiple modes. Here no number occurs more than once.

**There is no mode.**

(4) The midrange is the mean of the largest and smallest data points.

`"midrange"=(20+1)/2=10.5 `

These are all called measures of central tendency or measures of the middle.

**Sources:**

Given the data set 1,2,4,7,8,9,10,20:

(1) The mean (arithmetic mean) is the sum of the data divided by the number, n, of pieces of data.

Usually you report the mean to one more digit than the given data so

(2) The median is the number in the middle of the **ordered** data set. I.e. there are as many data points below the median as above the median.

Here the median is between 7 and 8; in the case that there is an even number of data points you take the mean of the two in the middle.

(3) The mode is the datum that occurs the most often. A set can have no mode, 1 mode, or multiple modes. Here no number occurs more than once.

**There is no mode.**

(4) The midrange is the mean of the largest and smallest data points.

These are all called measures of central tendency or measures of the middle.

**Mean** is the average of the entire data set.

1,2,4,7,8,9,10,20

= (1+2+4+7+8+9+10+20)/8

= 61/8

**= 7.625**

**Median** is the middle value of the entire data set.

1,2,4,**7,8,**9,10,20

In this case the total number of values is 8 therefore average is found for the 2 middle numbers 7 and 8

Median=(7+8)/2

=15/2

**=7.5**

**Mode** is the most repeated value of the data set.

1,2,4,7,8,9,10,20

Since in this data set no values are repeated therefore there will be no mode.

**Midrange **is the arithmetic mean of the maximum and minimum values of the data set.

1,2,4,7,8,9,10,20

= (1+20)/2

= 21/2

= **10.5**

`:.` **Mean= 7.625**

** Median= 7.5**

** Mode= none**

** Midrange= 10.5 Answer.**

Mean is another word for average. To find the mean of a set of numbers, all you have to do is add them together and divide by how many numbers you have in your set.

1+2+4+7+8+9+10+20=61

61/8=**7.625**

Median is the middle number in your data, when the data is in numerical order. You already have the numbers in order, so you just have to find the middle number. However, since there is an even amount, you have the numbers 7 and 8 as your middle numbers. Simply average them to get a median of **7.5**.

Mode is the number that occurs most in your set. Since no numbers repeat, you won't have a mode for this set.

Midrange is the average of the smallest number and the largest number.

20+1=21/2=**10.5**

The median would be the number lined up from lowest to highest in the middle, so in this case, 8 is the median. The mode is the number that appears most throughout the numbers listed, here this is no mode. To find the mean is to find the sum of all the numbers from the data and then divide by how every many numbers there are, 1+2+4+7+8+9+10+20=61/8= 7.6. The midrange is basically then of the largest and smallest numbers (range). In this case the midrange is 20+1/2= 10.5