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Monique

Member

Registered: 2007-02-17

Posts: 22

finding the mean, median and mode???

A census of 13 Year 1 classes in a school area give the following number of students in each class:

24   36   19   29   37   20   20   14   23   25   21   15   33

a)  how do I find the mean, median and mode of this data?

b)  and what sort of comment can I make on the differences between the answers I have calculated for the mean, median and mode?

a very exhausted and very fustrated Monique.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,412

Re: finding the mean, median and mode???

In probability theory and statistics, a median is a number dividing 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 are an even number of observations, one often takes the mean of the two middle values. Thus, when the given data is rearranged in ascending order, the arrangement would be
14, 15, 19, 20, 20, 21, 23, 24, 25, 29, 33, 36, 37.
It can be seen that 23 is the 7th and the middle term, hence 23 is the median.

Mean is defined as the average value. It is the sum of all the values, (24 + 36 + 19 + 29 + 37 +  20  + 20 + 14 + 23 + 25 + 21 + 15 + 33), divided by the number of values(13). In this case, it is 316/13=24.30769 or approximately 24.31.

The mode of a data sample is the element that occurs most often in the collection.
In the given data, the mode is 20, since it occurs twice and all others only once.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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pi man

Member

Registered: 2006-07-06

Posts: 251

Re: finding the mean, median and mode???

The mean of a group of numbers is what everyone usually calls the average.   Add up all your numbers and then divide that answer by the number of terms (13 in this case).

To find the median, rearrange your numbers from smallest to biggest.   The median will be the one in the middle.  You have 13 numbers to sort so one of them will be in the exact middle.   If you have an even number of terms, I think you take the mean (average) of the 2 middle terms.  For example:   2, 3, 5, 7, 8, 10    The two middle terms are 5 and 7 so the median is 6.

The mode is the number(s) which appears the most time.    In your group, it looks like 20 is the only one that appears more than once, so it's the mode.

Edited:  Once again, I'm just a little bit late.   Good work, Ganesh.

Last edited by pi man (2007-02-19 16:19:23)

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: finding the mean, median and mode???

Also: Mean Value, Median Value and Modal Value

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman