## Wednesday, May 5, 2010

### 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)

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.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?
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.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

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Other types of Representation

the following is the work completed by the various groups:

Data is based on class Birthdates
The mean =
The mode =
The median =

1. 1. Mean: The mean is the total numbers of the numbers divided by how many numbers are there.
Mode: The mode is the value that appears the most.
Median: The median is the middle value.
3. Mean: Add up these numbers: 2+3+4+7
Then divide the answer by the numbers are there: 16 divide 4 = 4
So the mean value is 4.
Mode: Put the numbers in order: 1, 5, 5, 5, 7, 9, 9
5 appear the most so the mode value is 5.
Median: Put the numbers in order: 1, 5, 5
The number in the middle is 5 so the median value is 5.
4. Mean: We use it when we want to combine average from samples of the same population with different sample sizes.
Mode: we use it when we want to make sure our estimates are correct.
Median: we use to to so called make sure our estimation are accurate, not more and not less

2. 1. -Median means the center/middle value
-Mode means the most common number
-Mean means the average

2. -Median : 7,3,6,2,4,5,1 put them in order and find the middle value
-Mode : 1,2,3,3,5 find the most common value which is the mode
-Mean : 1,2,3,4 add them all up and find the average.

3. -Median : Median is used to find the value of the middle item in a .
-Mode : To find which item is the most popular so we can buy that item.
-Mean : We use mean when we want to find average purchase price of a product.

3. Q1:Mean-The average value, calculated by adding all the observations and dividing by the number of observations.
Median

Middle value of a list. If you have numbers 2, 3, 4, 5, 6, 7, and 8, the median is 5. Medians are often used when data are skewed, meaning that the distribution is uneven. In that case, a few very high numbers could, for instance, change the mean, but they would not change the median.

Other definitions include the smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50%. But all mean the same thing in the end.
Mode-For lists, the mode is the most common (frequent) value.

Q3:Mean: 1+2+3+4=10 10/4=2.5 the mean value is 2.5
Mode:1,2,3,2,5,4,2 The mode is 2.
Median:1,2,2 Th median is 2.

Q4:Mean when we need to find the average.
Mode is when we want to answer faster.
Median:Check our estimation

4. Mean Average = Add up all the numbers / Amount of numbers
i.e. Mean average of 10, 22 and 50 is-:
10 + 22 + 50 / 3 = 27.333
We use mean average to find the class average marks of a test.

Mode Average = number that occurs most often.
i.e. Say we have numbers-: 1, 2, 2, 3, 5, 7, 7, 7, 8, 10
Mode is 7, as that occurs the most.
Mode average is used to find the most constant result in an experiment.

Median Average = The middle number
i.e. 1, 3, 5, 7, 9
Median would be 5, as it is the middle one.
For example, there are a row of trees of different heights. To find the tree whose height is the average of all the trees, median is used.

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6. Median is the middle of a list of ascending numbers.
1,2,3,4,5,6,7,8,9-5 is the Median.
Mean is the average.
1+2+3+4+5+6+7+8- 4.5
Mode is the highest frequency.
If we have the statistics of the grades. The number of students who got the grades.
A-5, B-7 , C-2, D-3, Failures- 1. B is the mode.

7. question 1

Mode-(Definiton)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(Definiton)median is described as the number separating the higher half of a sample, a population, or a probability
Mean-(Definiton)averageor approximating the statistical norm or average or expected value
Sources:
http://en.wikipedia.org/wiki/Mode_(statistics)
http://en.wikipedia.org/wiki/Median

question 3

Examples of mean:

Four tests results: 15, 18, 22, 20
The sum is: 75
Divide 75 by 4: 18.75
The 'Mean' (Average) is 18.75

(Often rounded to 19)

Examples of median:

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.

Examples of mode:

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)