## Thursday, April 29, 2010

### Chapter 16 : Data Handling Lesson 4

Dear 103s,

Welcome back from Common Test.

We are still in our study of Statistics.

Often we hear others compare a group of data using the MEAN, the MEDIAN and the MODE.

But what exactly is MEAN, MEDIAN, MODE?

Do an online search to find out about the meaning of MEAN, MEDIAN and MODE.
Post your findings under the Comment Section.
Please also include in examples on how you determine the MEAN, MEDIAN and MODE of a data set.

1. The "arithmetic mean" is the "average", whereby you add up all the numbers and then divide by the number of numbers. The "median" is the "middle value" in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list of values first. The "mode" is the value that occurs most often in the string of values. If no number is repeated, then there is no mode for the list of values.

Note: Getting a decimal value for the mean or for the median, if you have an even number of data points, it is perfectly alright. Don't round your answers to try to match the format of the other numbers.

Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

The median is the middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the
(9 + 1) ÷ 2 = 10 ÷ 2 = 5th number

13, 13, 13, 13, 14, 14, 16, 18, 21

So the median is 14.

The mode is the number that is repeated more often than any other in the above string of values, so 13 is the mode.

mean: 15
median: 14
mode: 13

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3. The mean is the average of a set of numbers. The median is the number in the middle of a sorted list of numbers. The mode is the number which appears most often in a set of numbers.

example :
4, 7, 14, 12, 6, 16, 7, 3, 8, 8

Mean = ( 3 + 4 + 6 + 7 + 7 + 8 + 8 + 12 + 14 + 16 ) ÷ 10 = 85 ÷ 10 = 8.5
Median = ( 8 + 7 ) ÷ 2 = 7.5
Mode = 7, 8

4. MEAN means the average, which is the following formula: total/number of numbers
(1+1+2+3+4)/5=2.2

MEDIAN is finding also the average, but in a different way, which is lining the numbers up in ascending order and taking the average number/numbers (if the number of numbers is even, take the middle 2 numbers).
(1+1+2+3+4)=2 (MEDIAN)

MODE is finding the average but in a different method. It involves taking the number repeated the most.
(1+1+2+3+4)=1 (MODE)

5. MEAN is to add up all the values in a set of data and then divide that sum by the numbers in the dataset.
MODE is the value that occurs most often. In this case, since
there are 3 90's, the mode is 90. A set of data can have more than one
mode
MEDIAN is the number in the middle. In order to find the median,
you have to put the values in order from lowest to highest, then find
the number that is exactly in the middle

6. MEAN: The average of numbers
MEDIAN: The middle value, so I'll have to rewrite the list in order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:

52, 13, 53, 15, 14, 14, 16, 18, 21

So the median is 14.

MODE: The mode is the number that is repeated more often than any other

7. MEAN is the average of a set of numbers.
Formula= Total sum of the numbers/Number of numbers.
Example: Three friends have a different number of chocolates, 1, 2 and 6 so it is 1+2+6=9. And now we divide it with 3 (the number of numbers) which leaves the answer as 3.

MEDIAN is the value in the middle which is lining them up in a descending order.
Example:
1
2
3
2 is in the middle so it is the MEDIAN. If there are 2 numbers like 2 and 3, slit them using MEAN like 2+3=5 then 5/2= 2.5

MODE is a value in a set of data that occurs most often.
Example:
1
2
3
3
3 is the value since it occurs the most.
{Under maintenance...}

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9. Mean, Median, Mode are three different kinds of averages.

Mean is the average that is found when you take the total value of the numbers dived by the number of numbers.
Example:
1+2+3+4+5+6=21
21/6=3.5

The median is the middle number.
Example:
1+2+3+4+5
Median=3 as it is the number in the middle

The mode is the number that appears the most in the list of numbers.
Example:
1+2+3+3+4+5
Mode=3 as it appears the most in the list.

Lucas Chia

10. Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are the most commonly used one.

The "mean" is the "average" , where you add up all the numbers and then divide by the number of numbers.
(Examples) The mean is the usual average, so:
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

The "median" is the "middle" value in the list of numbers. To find the median, the numbers have to be listed in numerical order.
(Examples) The median is the middle value, so the order is:
13, 13, 13, 13, 14, 14, 16, 18, 21

The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.
(Examples) The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.

mean: 15
median: 14
mode: 13
range: 8

11. To find the mean, you have to add up all the values in a set of data and then divide that sum by the number of values in the dataset.
Let's say you are writing about the World Wide Widget Co. and the salaries of its nine employees.

The CEO makes \$100,000 per year,
Two managers make \$50,000 per year,
Four factory workers make \$15,000 each, and
Two trainees make \$9,000 per year.

So you add \$100,000 + \$50,000 + \$50,000 + \$15,000 + \$15,000 + \$15,000 + \$15,000 + \$9,000 + \$9,000 (all the values in the set of data), which gives you \$278,000. Then divide that total by 9 (the number of values in the set of data).

That gives you the mean, which is \$30,889.
For the World Wide Widget Co., here are the worker's salaries:

\$100,000
\$50,000
\$50,000
\$15,000
\$15,000
\$15,000
\$15,000
\$9,000
\$9,000
That's 9 employees. So the one halfway down the list, the fifth value, is \$15,000. That's the median.
For the World Wide Widget Co., here are the worker's salaries:

The mode is the value in a set that occurs the most often.

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13. 1) THE MEAN
The mean is the average of the numbers: a calculated "central" value of a set of numbers.
It is easy to calculate: Just add up all the numbers, then divide by how many numbers there are.
Example: what is the mean of 4 ,2 and 3?
Add the numbers: 4 + 2 + 3 = 9
Divide by how many numbers (i.e. we added 3 numbers): 9 ÷ 3 = 3
So the Mean is 3.

2) MEDIAN
The middle number (in a sorted list of numbers). Half the numbers in the list are less, and half the numbers are greater.
To find the Median, place the numbers you are given in value order and find the middle number.
Example : find the Median of {12, 3 and 5}. Put them in order: {3, 5, 12}, the middle number is 5, so the median is 5.
If there are two middle numbers (as happens when there are an even amount of numbers) then average those two numbers.
Example: find the Median of {12, 3, 5 and 2}. Put them in order: {2, 3, 5, 12}, the middle numbers are 3 and 5, the average of 3 and 5 is 4, so the median is 4.

3) MODE
The number which appears most often in a set of numbers.
Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).

14. * wei chern you can't rip off the whole passage from the website.
the mean is the average of a set of numbers,like 15+2+3,meaning that the mean is 20/3 .

15. the median is the middle number of that group,which is divided like this:
high numbers | low numbers
15 | 2
________________3_________________
3 is in the center of this numbers, making it the median.

the mode is the most common of the numbers,soif the group is 2,3,4,5,6,6,6,6,6,6, the mode is 6.

16. 1-Mean
The mean of a list of numbers is the sum of all of the list divided by the number of items in the list or also know simply as average.
for example the mean of the below,
1,2,3,4=1+2+3+4=10
10/4 =2.5
2-Median
the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one.
for example,
1,2,3
As 2 is the middle of 1 and 3, it is the median.
if the numbers are 1,2,3,4,
there are two middle numbers, 2 and 3. The mean/average of the two numbers,
2+3=5, 5/2=2.5
the median is 2.5.
3-Mode
mode is the value that occurs the most frequently in a data set.
For example, 5 students took part in a test. Their scores are: 70,80,70,70,60.
As 70 is the most common number, it is the mode.

17. 1)Mean is the average
Eg.Four tests results: 15, 18, 22, 20
The sum is: 75
Divide 75 by 4: 18.75
18.75 is the Mean

2)The Median is the 'middle value' in your list.
Eg.
Find the Median of: 9, 3, 44, 17, 15 (Odd amount of numbers)
Line up your numbers: 3, 9, 15, 17, 44 (smallest to largest)
The Median is: 15 (The number in the middle)

3)
The mode in a list of numbers refers to the list of numbers that occur most frequently.
Eg.
Find the mode of:
9, 3, 3, 44, 17 , 17, 44, 15, 15, 15, 27, 40, 8,
Put the numbers is order for ease:
3, 3, 8, 9, 15, 15, 15, 17, 17, 27, 40, 44, 44,
The Mode is 15 (15 occurs the most at 3 times)

18. 1. Mean is the average of a set of numbers

2. Median is the number that is exactly right in the middle of the set of numbers

3.Mode refers to the numbers that has the highest frequency in the set of numbers

Example:

1,2,6,2,8,2,8

In this case, the mean is:
(1+2+6+2+8+2+8)÷7=4.14 (to 3s.f)

The median would be:
1,2,2,2,6,8,8 (Line up the numbers in ascending order)
The number in the middle is 2. Hence, the median is 2

The mode is:
1,2,2,2,6,8,8 (Line up the numbers so that it would be easier to see)

The number which has the highest frequency is 2. Hence, the mode is 2

19. 1) Mean: Mean is the arithmetic average of a set of values or distribution.
2) Median: A number which in the middle of a set of numbers.
3) Mode: Mode is the value that occurs the most frequently in a data set or a probability distribution

Examples:
1)Mean:12,15,16,26
Total value: 12+15+16+26=69
Mean value: 69/4= 17.25
thus 17.25 is the mean.

2)Median:16,26,12,15,24
Arrange in ascending order: 12,15,16,24,26
The number in the middle is 16. Terefore, the median is 16.

3) Mode: 12,12,13,14,16
The number which appear freuquently is 12. Therefore the mode is 12.

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21. If there is a string of numbers that has 10 (even) numbers, then to find the median, take the middle 2 numbers (of the string of numbers) and divide by 2 to find the median of the 10 numbers.

22. The mean is the sum of all of the list divided by the number of items in the list.
An example is the numbers 1,2 and 3. 1+2+3=6
6/the amount of numbers(3 in this case)=2
The median is the middle number in a set of numbers.
An example is, the numbers 50,27,30
line them up in accending order which will be 27,30,50
The median then is the number 30.
The mode is the number that occurs the most in a data set.
For example, the numbers 2,3,4,5,6,7,8,6,9
The number that occurs the most is 6 in this set of numbers. So 6 is the mode of that set of numbers.