### STATISTICS (ANALYSIS) : mean, mode & median

The Next Phase in Statistics is Data Analysis. In this segment we will be focusing on the following:
.1 Averages
.2 Histogram
.3 Other forms of presentation (Dot Diagram, Stem and Leaf)

----------------------------------------------------------------------------------------------------------
.1 Averages
'Before you can begin to understand statistics, there are four terms you will need to fully understand. The first term 'average' is something we have been familiar with from a
very early age when we start analyzing our marks on report cards. We add together all of our test results and then divide it by the sum of the total number of marks there are. We often call it the average. However, statistically it's the Mean!' [source: http://math.about.com]

1. Define the following statistical terms: Mean, Mode and Median
3. Provide an example on each of the terms
4. When do we use mean, mode or median?
----------------------------------------------------------------------------------------------------------
.2 Frequency Table and Histogram

Identify the characteristics of a Histogram.
What is/are the primary difference/s between Histogram and Bar Chart?

Do a simple survey in class and complete the following tasks
Complete a Frequency Table
• Use Numbers and Plot a Histogram (label the axes and provide a suitable Title)
• Find the (a) mean, (b) mode and (c) median
• Which of the above averages ie. mean, mode or median you think best represents your findings about your survey? Why?

Group 1: Birth months of all your classmates
Group 2: Home location of all your classmates (North, South, East, West)
Group 3: Number of siblings of individual student
Group 4: Types of CCA
Group 5: Favourite genre of movies: Horror, Comedy, Thriller, etc etc

----------------------------------------------------------------------------------------------------------
Other types of Representation

1. MEAN : The mean is the total of the numbers divided by how many numbers there are.

MODE : The mode is the value that appears the most.

MEDIAN : The median is the middle value.

2. Mean

The average value, calculated by adding all the observations and dividing by the number of observations.

Median

Middle value of a list of numbers.

Mode

For lists, the mode is the most common (frequent) value.

3. Mean - Total sum divided by quantity of integers.

Mode - Most frequent number in a data set.

Median - Middle value that separates the greater and lesser halves of a data set.

4. Mean:the sum of all the numbers divided by the no. of numbers there are

Mode:the number that appears the most

Median:
-if the total amount is odd,the number in the middle of the list is the median
-if the total amount is even,the two numbers in the middle must be added together and divided by two to get the median

5. In mathematics, we normally consider average as the sum of all values divided by the number of values added. Strictly speaking, it is the ‘arithmetic mean’, or simply referred to as the ‘mean’. The mean is almost considered synonymous with average, but statisticians will definitely disagree, because, in essence, mean is only a form of describing an average.

eg. a boy has 1 toy, another has 3 toys.
the mean is 1+3=4 4/2=2 the mean is 2.

Median-

Median is the central point of the set. In statistics, it is usually the number that occurs in the middle of a set of numbers. A description of the average can be in the median, some of the time, if it is considered as the most suitable way to describe the central tendency of a particular sample.

Read more: Difference Between Average and Mean | Difference Between http://www.differencebetween.net/science/difference-between-average-and-mean/#ixzz0nDGX0m4s

Mode-

value that occurs the most frequently in a data set or a probability distribution.

Example: 1, 2, 2, 3, 4, 7, 9, result: 2

6. Mean=Average value of the sum numbers divided by the amount of numbers.

1+2+3=6
6/3=2(Mean)

Median= The number which is in the middle of a lists of number.

1 2 3 4 5 6 7
4=Median

Mode=The number that is the most seen in a bunch of numbers.

1 2 3 4 4 5 6 7 8

4=Mode

7. Mean: The mean is when a list of numbers is the sum of all of the list divided by the number of items in the list.

Median: The median is the middle number of the group when they are ranked in order. It is used most often when the distribution of the values is skewed with some small numbers of very high values, as seen with house prices or incomes.

Mode: The mode is the value that occurs the most frequently in a data set or a probability distribution. It has the advantage that it can be used with non-numerical data (e.g., black cars are most frequent), while other averages cannot.

8. Mean: It means the average of a number of different amounts

Median: It means the middle value of a set of numbers arranged by lowest to highest.

Mode:It means the number which occurs the most.

9. The MEAN is the arithmetic average, the average you are probably used
to finding for a set of numbers - add up the numbers and divide by how
many there are: (80 + 90 + 90 + 100 + 85 + 90) / 6 = 89 1/6.

The 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:

80 85 90 90 90 100
^
The 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.

10. Mean: Average of two or more numbers.

Median: The midpoint of a group of numbers that are arranged in order of value.

Mode: The most common term in a set of numbers.

11. Mean:

In mathematics, we normally consider average as the sum of all values divided by the number of values added. Strictly speaking, it is the ‘arithmetic mean’, or simply referred to as the ‘mean’. The mean is almost considered synonymous with average, but statisticians will definitely disagree, because, in essence, mean is only a form of describing an average.

Read more: Difference Between Average and Mean | Difference Between http://www.differencebetween.net/science/difference-between-average-and-mean/#ixzz0nDGX0m4s

eg. a boy has 1 toy, another has 3 toys.
the mean is 1+3=4 4/2=2 the mean is 2.

Mode:

value that occurs the most frequently in a data set or a probability distribution.

Example: 1, 2, 2, 3, 4, 7, 9, result: 2

Median:

The middle value.

12. MEAN: The mean is what you get when you add the values together and divide by their quantity. Eg. There are a total of 23 students in 1-02. The total height of all the students in 1-02 is 30.5m. To find the mean height, we take 30.5m divide by 32

MODE:The value that appears most in the data collected.
E.g Sizes were measured and they took the size which has the most number of students suitable for that size

MEDIAN: A median is the value of the biggest number+smallest number divide by 2.
E.g The height of the buildings are 100m, 250m and 350m respectively, the median of the buildings is 350m+100m=450 450/2=225

13. Mean is the average, mean is sumo f values over number of values.
Example:3,5,7,3,5 the mean will be 23(sumo f values) and 5 (number of values)23 divided by 5 is 4.6 which is the mean.

Mode is usually the often number seen
Example:3,4,5,5,6,7 the mode will be 5

Median is the middle number
Example:4,1,2,10,8,6,7 rearranged to 1,2,4,6,7,8,10 and finally we can say the median is 6

14. Mean: (Normal way of finding average) Add all the numbers and divide
by the number of numbers.
Ex: 1, 4, 6, 9. The mean is 5.

Mode: The number that repeats the most in the set of numbers.
Ex: 1, 3, 5, 5, 5, 6, 6, 9. The Mode is 5.

Medium: The number that is in the exact middle of the set of numbers.
Ex: 10, 15, 20, 25 The Medium is 17.5.

15. This comment has been removed by the author.

16. This comment has been removed by a blog administrator.

17. 1. Mean: The mean is the total amount of all the numbers divided by the number of numbers.

Mode: The mode is the number with the highest frequent rate.

Median: The median is the number in the middle or the average of the two numbers in the middle.

3. Mean: To find the mean of 5, 6 and 7, add 5, 6 and 7 together then divide by 3.

5+6+7=18
18/3=6
The mean is 6.

Mode: To find the mode of 7, 8, 8, 9, 9, 9, 10, 10, find out the number with the highest frequent rate.

The mode is 9.

Median: To find the median of 7, 8, 10 and 11, add 8 and 10 together and divide it by 2.

8+10=18
18/2=9
The median is 9.

4. Mean: We use mean when we want to find out the average.

Mode: We use mode when we want to find out the number with the highest frequency rate.

Median: We use median when we want to find out the middle number.

18. Median
The Median is the "middle number" (in a sorted list of numbers).
Example:

3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29
If we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
There are fifteen numbers. Our middle number will be the eighth number:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
The median value of this set of numbers is 23.
Mean

The mean is just the average of the numbers.
Example:
What is the Mean of these numbers?
6, 11, 7
Add the numbers: 6 + 11 + 7 = 24  Divide by how many numbers (ie we added 3 numbers): 24 ÷ 3 = 8
The Mean is 8
Mode
The mode is simply the number which appears most often.

Example:

To find the mode, or modal value, first put the numbers in order.
Look at these numbers:
3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29
In order these numbers are:
3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 29, 39, 40, 56
This makes it easy to see which numbers appear the most.
In this case the mode is 23.

19. (Done By:Yi Lin & Jaime)
Histogram is...
a bar chart representing a frequency distribution; the area is equal to the frequency of the interval
Difference between a bar graph and a histogram...
The area in a histogram represents the frequency but the height is used to represent data in a bar graph

20. MEAN: The arithmetic mean is the "standard" average, often simply called the "mean".
Mode: In statistics, the mode is the value that occurs the most frequently in a data set or a probability distribution. In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score.
Median: In probability theory and statistics, a median is described as 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. If there is an even number of observations, then there is no single middle value, the median is defined to be the mean of the two middle values.....:D
YOU'LL NEVER WALK ALONE

21. Mean is another word for average.
Median is the number in the middle.
Mode is the number that appears the most.

An example of mean is the average score of the class in an exam.
An example of median is the out of 55, 56, 57 and 58 the edian is 56.5.
An example of mode is
55 56 57
IIII II III
So, 55 is the mode.

We use mean when we want to find the average of something to compare a big group of people to another big group of people.
We use median to find the middle one.
We use mode to find the one with the most frequency.

22. Q1)

Mean: It is the average, which is the total sum of numbers divided by how many numbers there are.

Mode: It is the most populated choice.

Median: It is the number that is in the middle.

Q3)

MEAN

Eg. Given the numbers, 4, 5, 6, 7, 8, find the mean of the numbers.
Mean= 4+5+6+7+8
=30(sum of all numbers)
30÷5(total number of numbers)
=6(mean)
Ans: 6

MODE

Eg. In ABC company, two employees earn \$600, four of them earn \$900, and three of them earn \$700. Find the mode.
The mode is \$900, as it has the most number of employees earning that amount.

MEDIAN

Eg. Find the median of 5,6,7,8,9(total number of numbers, 5, which is an odd number)
7 would be the answer, as it is the middle number.
If there are an even number of numbers, eg, 5,6,7,8,9,10. Take the two middle numbers, 7 and 8, add them together then divide. The answer would be 7.5.

Q4)

When do we use mean, mode or median?

We use the mean to find out the average usually for data collection.

We use mode to decide which is the most populated choice or the number with the highest frequency rate

We use the median when we want to find the middle value/number.

23. Example:1,2,3,4,5,6,7,8,9,10
Mean:
The mean would be 27.5
The mean is the sum of all the numbers divided by the number of numbers...
Median:
The median is 5
The number at the middle of the whole string of numbers
Mode:
There would be no mode as it is the most frequent value and all of the numbers only appear once

24. 1. Define the following statistical terms: Mean, Mode and Median
3. Provide an example on each of the terms
4. When do we use mean, mode or median?

Mean means the average (eg) of the total divided by the number of people.

For example, we have 3 people with heights of 1.6m, 1.7m and 1.8m respectively. The average height of the people is (1.6m + 1.7m + 1.8m) ÷ 3 = 1.7m.

We use mean when we want to find the average of some objects.

Median means that the middle number (when odd number) when arrange in ascending or descending order OR the average of the 2 middle numbers (when even number).

For example,
1st scenario: We have 3 buildings with heights of 7m, 5m and 9m respectively. So first, we arrange them in either ascending or descending order. In this case, we arrange them in ascending order: 5m, 7m, 9m. The middle number is 7m. So the median of the 3 buildings is 7m.

2nd scenario: We have 4 buildings with heights of 7m, 10m, 3m and 15m respectively. So first, again, we arrange them in either ascending of descending order. In this case, we arrange them in descending order: 15m, 10m, 7m, 3m. The median is the average of the 2 middle numbers, which is in this case, 10m & 7m. The mean of 10m & 7m is 8.5m. So the median of the 4 buildings is 8.5m.

We use median when we want to find out the middle number of a particular object.

Mode means the object with the highest frequency number, where we compare the results.

For example:

We are doing a survey about the shoe size that 25 customers would buy. The following are the shoes size number followed by the number of customers who gave their shoe size:

33 - 3
34 - 8
35 - 5
36 - 7
37 - 2

We first, to make our job easier, either arrange them into a table or arrange them in ascending or descending order. In this case, we arrange them in ascending order according to the number of orders. So now:

37 - 2
33 - 3
35 - 5
36 - 7
34 - 8

Now that it is in ascending order, it is quite obvious that if they are buying, there are more orders for size 34. So the cobbler should produce more of size 34, followed by size 36, 35, 33 and 37.

We use mode when we want to find out which product we should produce more so satisfy the customers' needs.

--Su En