## Friday, May 7, 2010

### Chapter 16 : Data Handling Lesson 4

Dear 107s,

We are still looking at Statistics at the moment.

Often when we compare data, we heard about people comparing the MEAN, the MEDIAN and the MODE.

Thus what does this terms actually means?

Do an online search on the meaning of MEAN, MEDIAN and MODE and input the meaning under the comment section. Please also include in examples on how to determine the MEAN, MEDIAN and MODE in a data set.

1. The mean is known as the average and it is the sum of all scores over the number of scores. The median is known as the distribution of the middle and is used to determined the value of a number. THe mode is the most frequently occurring score.

2. The term, 'Mean', means the average. It is calculated by adding the sum of all the numbers, and then dividing it by the number of numbers there are.
The term, 'Median', means the middle entry in the list of numbers.
The term, 'Mode' means the number that most frequently occurs.

3. 'Mean' is known as an average and is obtained by dividing the total sum of numbers by the amount of numbers.
'Median' is the middle entry of a list of either odd or even numbers.
'Mode' is the specific number that appears in a list of numbers the most amount of times.

4. This comment has been removed by the author.

5. Mean, median, and mode are three kinds of "averages".
The "mean" is the "average" you're used to, where 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.
The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

6. MEAN means the total amount of something divided by the number of groups of that something,which is the average we are using now.For example,if you have 2 classes with 21 and 23 students in each and want to find the mean number of students in each class,you add 21+23=44 and 44/2 to find the mean.
MEDIAN means the number that is closest to the middle.You list out the numbers in numerical order and see which number is in the middle.If you have an odd number of numbers,you see which number at the end is too small or too big to be included in the list.
MODE means the value that appears the most in the list of values.For example in a class of 16 boys and 5 girls,the mode gender of the students in the class is male.

7. Mean is the average of numbers, which is the sum of all of the list divided by the number of items.

Median is the "middle number" (in a sorted list of numbers). To find the Median, we place the numbers we are given in value order and find the middle number.

Mode is simply the number which appears most often. To find the mode, or modal value, first put the numbers in order.

8. Mean is the average of a group of numbers. To determine the mean, simply divide the sum of the numbers with the number of numbers.

Median is the number(s) in the middle, after arranged in ascending order. To determine the median, arrange the numbers in ascending order then determine the number in the middle of the series. If there is an even number of numbers, find the average of the two middle numbers.

Mode is the number that appears most frequently in a series of numbers. To find the mode, simply arrange in order, for convenience, then pick out the number with the most repeat. There can be more than 1 mode, but if there are no repeat in the series, there is no mode in it.

Hao Yang

9. The definitions of:
Mean- average: approximating the statistical norm or average or expected value
Median- A statistical term and is the value above which 50% of the other values lie and below which 50% of the values lie or is the middle value in a series of values.
Mode- the value that occurs most frequently in a given set of data

10. Mean is the average of a particular group of numbers and to get it you must divide the sum of all the numbers by the total number of numbers.

Median is a value/number that is the midpoint of a distribution of frequency in a set or series of numbers/values such that there is an equal chance of falling below or going above it.

Mode is the value that is seen most in a given set of numbers/values

11. mean is the average value of a group of numbers, to get it, just divide the total of the group of numbers by the total amount of numbers in the number group.

median is the number in a group of numbers that when arranged in ascending order, it is directly in the middle in terms of value.

mode is the number that is seen the most in a given set of numbers

12. 'Mean' means the average. Example: If a packet of 15 sweets were to be given out to five boys unequally, what would be the mean number of sweets that each boy will get? To calculate the mean, you just have to divide 15 by 5 to get 3.

'Median' is the number right in the middle of a series of numbers.

'Mode' is the value that appear the most number of times in a set of data.

For this post on Data Handling Lesson 4,...

Mean, median and mode are all part of statistics and can be quite similar to each other, depending on the data given.

This comment will talk about more details on these three mathematical terms in statistics.

1. MEAN
Basically, in simple terms, the mean is actually the average of the all the integers in the data, that is the division of the total number of the integers by the sum of all the integers.

eg. When the represented unknowns are arranged such that the larger the alphabet the larger the integer, Mean of e+c+d+d+b+a+f = (e+c+d+d+b+a+f)/7 (because there are 7 integers altogether.)

An example of how Mean can be used in daily lives would be in the results of the students' test scores in a class. By calculating the mean of the results of all the students in the test, a teacher would be able to know his/her progress in teaching the class compared to the other classes. (teachers always compare us to other classes.)

eg. There are 21 students in a class and their scores in a 21-mark test is 17,9,16,12,3,5,7,19,6,21,14,8,20,1,4,10,2,15,18,13 and 11 respectively. The mean of the results of all the students is hence the division of the total number of the integers by the sum of all the integers, which is (17+9+16+12+3+5+7+19+6+21+14+8+20+1+4+10+2+15+18+13+11)/21=11

Mean of results = 11

2. MEDIAN
The median is similar to the mean that it can also be considered a type of average, but that it is the definition of having the strict rule of arranging all the values of all the integers in order first before selecting the integer in the middle of all the other integers, thus dividing the remaining two groups of integers into greater halve and the smaller halve.

eg. When the represented unknowns are arranged such that the larger the alphabet the larger the integer, Median of e+c+d+d+b+a+f = middle integer of a+b+c+d+d+e+f (arranging in order) = d (middle integer)

But what happens when the total number of integers are not even? In this case shown below, the median of the integers will be the mean of the two middle integers.

eg. When the represented unknowns are arranged such that the larger the alphabet the larger the integer, Median of e+c+d+d+b+a+f+g = mean of middle integers of a+b+c+d+d+e+f+g (arranging in order) = d+d/d (mean of middle integers)= 2 (because 2d/d = 2)

An example of how Median can be used in daily lives would be in the results of the students' test scores in a class. By calculating the median of the results of all the students in the test, students will be able to know their their positions in class(students always like to compare between 'higher positions'.)

eg.There are 21 students in a class and their scores in a 21-mark test is 17,9,16,12,3,5,7,19,6,21,14,8,20,1,4,10,2,15,18,13 and 11 respectively. The median of the results of all the students is hence arranging all the values of all the integers in order first before selecting the integer in the middle of all the other integers, which is the middle of 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21. (arranging) There are 21 integers altogether. Therefore, excluding the middle number, there will be 10 numbers in each group (21-1)/2=10. 10+1 or 21-10=11.

Median of results = 11

TAKE NOTE that in this case, the median and mean of the same students' results is exactly the same because of the fact that the data is given in a sequence.

Therefore: When the integers in a data is in a sequence of an odd number of consecutive numbers side by side, the median of this set of data is the same as the mean.

TAKE NOTE that the median and mean of the data is also the same when all the numbers in the set are the same. (This is actually very obvious and does not need to be stated)

(To be continued...)

14. (continued from part 1...)

3. MODE
This last mathematical term is used to describe the integers which appear most frequently in a set of data. It is better to arrange the integers which come out most frequently together but still, the most basic way of calculating the mode of the data is...just by looking at the integer(s) which appears the most number of times! (unless...you cannot differentiate between different numbers)

eg. When the represented unknowns are arranged such that the larger the alphabet the larger the integer, Mode of e+c+d+d+b+a+f = d (because d appears most frequently in the set, just by seeing!)

But what happens when there are 2 numbers which appear most frequently in the set? In this case, the data set would be known as bimodal and to solve the problem of having 2 numbers which appear most frequently in the set is...just by having 2 modes in the set.

eg. When the represented unknowns are arranged such that the larger the alphabet the larger the integer, Mode of e+c+d+d+b+a+a = a and d (because both a and d appears most frequently the same number of times)

TAKE NOTE that the mode of a data set can be 0 (eg. in temperatures) but a mode of 0 doesn't mean no mode. A data with no mode is used to describe a set of data which all the numbers appear the same number of times (eg. one time for each number)

An example of how Mode can be used in daily lives would be in the results of the students' test scores in a class. By the calculation of mode, students will be able to know how many of them scored the same marks. (students always like to compare in "Hi-5! We got the same marks") Of course, when integers come out frequently many more times than the others, mode will be able to be used to calculate the scores which most students...scored.

eg.There are 21 students in a class and their scores in a 21-mark test is 17,9,16,12,3,5,7,19,6,21,14,8,20,1,4,10,2,15,18,13 and 11 respectively. But after that, teachers realised that they had given oneless mark to the student with 1 mark. (Teachers often make mistakes in the tests of students) As a result the new scores of the students in the class are as follows:
17,9,16,12,3,5,7,19,6,21,14,8,20,2,4,10,2,15,18,13 and 11. The mode of the results of all the students is hence by arranging the numbers which come out most frequently in the set first so that it is easier to 'work out' the mode, (In fact, by arranging the numbers, you are already working out the mode of the numbers because it is obvious that if an integer comes out frequently 2 times and the other comes out 3 times, the integer which comes out 3 times in the set is the mode.), which is the number which comes out most frequently in "17,9,16,12,3,5,7,19,6,21,14,8,20,2,4,10,2,15,18,13 and 11" = the number which comes out most frequently in "17,9,16,12,3,5,7,19,6,21,14,8,20,2,2,4,10,15,18,13 and 11" (the integers coming out most frequently are arranged and it was noticed that 2 times of 2s were found in the set compared to the others which only comes out once)

Therefore, mode of the new results of the students = 2

(to be continued...)

15. (continued from part 2...)

4. THERE IS NO '4'
Well, this is the end of my comment on this post and here are some of the references which I used:

a)http://www.investorwords.com/3030/median.html
b)http://en.wikipedia.org/wiki/Mode_(statistics)#Comparison_of_mean.2C_median_and_mode
c)http://www.mathgoodies.com/lessons/vol8/mode.html

And, the website used to generate the random scores of the students is: random.org.
If you have any other enquiries on this post, please refer to the other comments.

Thank you all comment readers and have a nice day.

Yours mathematically,
NWH - Neo Wei Hong (14),
of SST S1-07,
Currently commenter of this post,
With special thanks to Mr Edmund Ng.
(A signature cannot be put here)

Email: Not required
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Except for the addresses of the references which I used, no 'copy-and-paste's are used in this post.
END OF COMMENT

(This comment has to be broken into 3 parts because when I written it as one or two, this sign appear below the 'Post Comment' button which read "! Your HTML cannot be accepted: Must be at most 4,096 characters)

16. The mean is the STATISTICAL word for average, for example :
Four tests results: 15, 18, 22, 20
The sum is: 75
Divide 75 by 4: 18.75
The 'Mean' (Average) is 18.75
The Median is the 'middle value' in your list. When the totals of the list are odd, the median is the middle entry in the list after sorting the list into increasing order. When the totals of the list are even, the median is equal to the sum of the two middle (after sorting the list into increasing order) numbers divided by two. Thus, remember to line up your values, the middle number is the median! Be sure to remember the odd and even rule.
Examples:
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)
Find the Median of: 8, 3, 44, 17, 12, 6 (Even amount of numbers)
Line up your numbers: 3, 6, 8, 12, 17, 44
Add the 2 middles numbers and divide by 2: 8 12 = 20 ÷ 2 = 10
The Median is 10.
The mode in a list of numbers refers to the list of numbers that occur most frequently. A trick to remember this one is to remember that mode starts with the same first two letters that most does. Most frequently - Mode. You'll never forget that one!
Examples:
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)
*It is important to note that there can be more than one mode and if no number occurs more than once in the set, then there is no mode for that set of numbers.

17. The "mean" is the sum of the group of numbers divided by the number of numbers in the group.

The "median" is the numeric value separating the higher half of a value (e.g. population) from the lower half.

The "mode" is the number that appears most in an observation.