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2.5 Measures of Central Tendency (Mean, Median and Mode)
What does mean, median and mode mean?
Mean
Examples
Example 1: The number for of baskets scored by each player in a basketball team, in one outstanding game, had been recorded in the following table: (Note: The is a sample because it is not all the members of the team. only the a select few were chosen to analyze)
a) What is the average?
Since the question stated that the data collected was a sample, the following formula is used:
THEREFORE: the average points scored per player, is 13.
Mean
- The “average” of the set of data points
- Population:
- Sample:
- refer to example 1 a and 2 b
- the median is the middle value of a set of data
- the set of data must be arranged in oder, from highest to lowest, or visa versa
- If there in even number of data points:
- Take the average of both middle points
- refer to example 1 b
- The value in a set of data points that is repeated most
- refer to example 1 c
- Used to calculate an average of a set of data when some values are more important than others (i.e ones calculated average)
- Equation:
- refer to example 2 b
- To organize group data; organize the data into intervals
- Equation:
Outliers
- What is an outlier?
- an outlier is a data point that is drastically different from the rest of the collected data
- refer to example 3
Examples
Example 1: The number for of baskets scored by each player in a basketball team, in one outstanding game, had been recorded in the following table: (Note: The is a sample because it is not all the members of the team. only the a select few were chosen to analyze)
| Players Name | Number of Points Scored |
| D’Onfrio | 25 |
| Maxin | 20 |
| Richardson | 17 |
| Killip | 12 |
| Lawson | 0 |
| Mecado | 19 |
| Pederson | 8 |
| Tomasovic | 5 |
| Durham | 12 |
| Lobo | 10 |
Since the question stated that the data collected was a sample, the following formula is used:
THEREFORE: the average points scored per player, is 13.
b) What is the median?
0 5 8 10 12 12 17 19 20 25
Since there is an even set of data points, the average of the two middle numbers much be taken:
THEREFORE, the median baskets scored is 12 points.
0 5 8 10 12 12 17 19 20 25
Since there is an even set of data points, the average of the two middle numbers much be taken:
THEREFORE, the median baskets scored is 12 points.
c) What is the mode?
0 5 8 10 12 12 17 19 20 25
12 is the only number repeated more than once
THEREFORE, the final mode of this set of data is 12 points.
***NOTE: It is possible to get the same mode and the same median. It is also possible to get more than 1 mode. ***
Example 2: Bob is applying to engineering this year, and wants to calculate his average. The following is a summary of his marks, and the weight factor the university uses. (Note: This is a sample because it is not all of his marks; he decided to take eight courses this year )
a) What is the un-weighted mean?
Since the question asks for the UN-WEIGHTED mean, the simple sample equation is used:
THEREFORE, the un-weighted mean is 86%
0 5 8 10 12 12 17 19 20 25
12 is the only number repeated more than once
THEREFORE, the final mode of this set of data is 12 points.
***NOTE: It is possible to get the same mode and the same median. It is also possible to get more than 1 mode. ***
Example 2: Bob is applying to engineering this year, and wants to calculate his average. The following is a summary of his marks, and the weight factor the university uses. (Note: This is a sample because it is not all of his marks; he decided to take eight courses this year )
| Subject | Mark | Weight factor |
| Discreet Math (requirement) | 90% | 3 |
| Calculus (requirement) | 89% | 3 |
| Physics (requirement) | 88% | 2 |
| Data Management (requirement) | 85% | 3 |
| English (requirement) | 70% | 4 |
| Philosophy (elective) | 94% | 1 |
Since the question asks for the UN-WEIGHTED mean, the simple sample equation is used:
THEREFORE, the un-weighted mean is 86%
b) What is the weighted mean?
Since the question asks for the WEIGHTED mean, the following equation is used:
THEREFORE, the weighted mean is 87%.
Since the question asks for the WEIGHTED mean, the following equation is used:
THEREFORE, the weighted mean is 87%.
c) Is there a difference? Explain why a university would place a weight factor.
There is a difference is the weighted and un-weighted mean. In the un-weighted mean, the average was 86%; in the weighted average, the average was 87%. A university would place a weight factor on the requirements because some courses are more “program” specific than others. Due to this, the university places importance on these marks, more than other electives.
Example 3: The following are heights of 6 individuals in Mr. Lawson's third period class.
There is a difference is the weighted and un-weighted mean. In the un-weighted mean, the average was 86%; in the weighted average, the average was 87%. A university would place a weight factor on the requirements because some courses are more “program” specific than others. Due to this, the university places importance on these marks, more than other electives.
Example 3: The following are heights of 6 individuals in Mr. Lawson's third period class.
Name Height (Inches)
Bob 61
Tina 66
Karen 62
Lucy 65
Jeffery 61
Andrew 81
Bob 61
Tina 66
Karen 62
Lucy 65
Jeffery 61
Andrew 81
Which height would be considered an outlier?
Andrew's height would be considered the outlier because it is so distant from the rest of the data. All the other students have a height between 61-65 inches. Andrew is a lot taller than the rest of his class!
Andrew's height would be considered the outlier because it is so distant from the rest of the data. All the other students have a height between 61-65 inches. Andrew is a lot taller than the rest of his class!
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| Started By | Thread Subject | Replies | Last Post | ||
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| Anonymous | Find Measures of Central Tendency in a HP calculator | 1 | Aug 3 2009, 6:30 AM EDT by Anonymous | ||
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Thread started: Aug 7 2008, 12:16 AM EDT
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If you have a HP49G+ or HP50G calculator you can find Measures of Central Tendency and many others with the library 1042: statdes V1.02 in my page:
http://cesarv.wetpaint.com/page/L1042+STATDES |
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| Mr._D'Onofrio | very nice! | 1 | May 5 2008, 11:39 AM EDT by Anonymous | ||
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Thread started: Apr 26 2007, 9:15 PM EDT
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I really like the overall look and explanations of this page. I find, however, your explanation of median unclear. Also, why are examples 1 and 2 samples. Could you please explain?
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| Mr._D'Onofrio | assessment (oops, I forgot) | 0 | May 15 2007, 10:28 AM EDT by Mr._D'Onofrio | ||
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Thread started: May 15 2007, 10:28 AM EDT
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Your choice of tags is very good.
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