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statistics

I have done a survey and I need to calulate the mean, median and mode for my data.  To try and determine an average divorce rate I interviewed 15 married people, 8 females, 7 males.  I asked each person how many times they had been divorced.  10 people said 0, and 5 people said 1.  I am unsure how to caculate the mean, median and mode with this data.  Please help.

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The mean is the average.  This is where you find the sum of your data, and then divide by the number of people you surveyed.


(10x0) + (5x1) = 5

5/15 = 1/3 = 0.33

 

To find the median you list your data in ascending order, and find the number that is is the middle.

 

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1

 

In this case, the median would be 0.

If there were an even number of data points, for example if there were 4 who said 0, 6 who said 2, you would find the mean of the two center numbers.

 

0, 0, 0, 0, 2, 2, 2, 2, 2, 2

2 + 2 = 4

4/2 = 2

In this case the median would be 2.

 

The mode is found by determining which data point is most frequently expressed.  So, in the case where 10 said 0, and 5 said 1, the mode would be 0.

In the second example I suggested where 4 said 0, and 6 said 2, the mode would be 2.

 

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2 Answers

Hi Pam. I see you edited your question. Let me adjust my answer.

The mean is the sum of all your data divided by the number of data points. You have 15 answers. The sum is 10 x 0 + 5 x 1 = 5 divorces.

5/15 = 1/3 ≈0.33. This is your mean divorce per person.

To get the median, line up the data in order and find the middle data point:

0, 0,0,0,0,0,0,0,0,0, 1, 1,1,1,1

0 is in the middle and is the median. The mode is the most frequent occurring data point--in this case, 0 occurs 10 times, which is more than any other value. 0 is your mode.

Old answer (when you had yes/no data):

You have categorical data. No mean or median can be determined. The mode is simply the most frequent response. In your case, the mode is "NO, I have not been divorced." That's all there is to it.

The median and the mean can ONLY be determined if there is a quanitative component to your variables. For example, you could have asked "How many times have you been divorced?" The people surveyed could say 0, 1, 2, 3, 4, and so on. This would be discrete quantitative data that does have a mean and a median. But that is not what you presented here with your "yes/no" data.

 

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This data set has no numerical values, just qualitative responses ('divorced/ not divorced') so it does not really lend itself to the traditional understandings of mean, median, and mode that you would use to calculate an average divorce rate. But a very liberal interpretation is below!!
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The mean is the average. Since you interviewed 15 people and 5 said they had been divorced, the mean divorce rate is 5 of 15 = 5/15 ≈ 33.3%. But more generally, to calculate a mean of a set of numbers add up all the numbers and divide by the number of values.

The median of a numerical data set (that is organized from least to greatest) is the middle value. Since this data set does not have numbers, the median is not really well-defined. The only way that I see to force a median here is to assign numbers. Divorced = 1, Not divorced = 0. So your data set is {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1} to represent 10 non-divorced, and 5 divorced. The median (middle number) is 0. So your median is "Not divorced." (Again, not a good measure here.)

Likewise, the nature of your survey does not lend itself to a natural mode, which is just the most frequently ocurring value. Your most frequent response was "not divorced." So that is your mode. (But like median (and mean), mode would work better with number values rather than qualitative responses like "not divorced.)
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If you want to design a survey to calculate average divorce rate, you might look at divorce rates of several different countries. For example, for six countries, the divorce rates, in percents, are given by:
{20, 25, 26, 30, 38, 50}

  • Mean: (20 + 25 + 26 + 30 + 38 + 50)  / 6 = 31.5
  • Median: 26 & 30 are both in the "middle", so the median is the average of 26 & 30, or 28
  • Mode: No number occurs more frequently than any other, so there is no mode. If there were 2 26's and only one of every other number, the mode would be 26.