Statistics - properties of the mean

In summary, the question asked the student to compute the mean, and then to compute it again with an additional observation of zero. The mean in this case is not robust, as the addition of a single observation of zero significantly affects its value.
  • #1
pointintime
166
0

Homework Statement



not exactly sure were this goes

ok there was a question that my teacher told me i got wrong

the question asked me to compute the mean which I did...

then the question went on to tell me compute the mean with another observation equal to zero

then the part that he drew the line through was my response to this question

Write a sentence about the effect of the zero on Joey's quiz average that mentions this property...

my response

The property that this illustrate of the mean is the observations. Sense the number of observations increased but the sum of the observations stayed the same this brough down the mean by defintion...

ok he drew a line threw it and told me it was wrong so my question is how is this wrong?

What would a correct answer include?

Thanks for any Help!

Homework Equations





The Attempt at a Solution

 
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  • #2
Hi pointintime! :smile:
pointintime said:
my response

The property that this illustrate of the mean is the observations. Sense the number of observations increased but the sum of the observations stayed the same this brough down the mean by defintion...

ok he drew a line threw it and told me it was wrong so my question is how is this wrong?

hmm … the English is bad (but I assume it's a translation?), but apart from that, it looks basically correct …

as you say, the mean is the total divided by the number of observations, and the total stays the same but the number of observations increases. :smile:
 
  • #3


The answer the OP gave was probably taken by the instructor to be an observation of the change in this particular case. I think the "property" statement would center on the fact that the mean is not robust (not sensitive, not resistant, depending on the selected terminology); its value can be significantly influenced by a single measurement.
 

1. What is the mean in statistics?

The mean is a measure of central tendency in statistics that represents the average of a set of data. It is calculated by adding all the values in a data set and dividing by the total number of values.

2. How is the mean affected by outliers?

The mean is greatly affected by outliers, which are extreme values in a data set that are significantly higher or lower than the rest of the data. Outliers can pull the mean in their direction, making it an inaccurate representation of the data.

3. What is the difference between the arithmetic mean and the geometric mean?

The arithmetic mean is the sum of all values in a data set divided by the total number of values, while the geometric mean is the nth root of the product of n numbers. The arithmetic mean is used for numerical data, while the geometric mean is used for data that follows a multiplicative pattern, such as growth rates.

4. Why is the mean sensitive to sample size?

The mean is sensitive to sample size because it takes into account every value in a data set. As the sample size increases, the mean becomes a more accurate representation of the population. However, with a smaller sample size, the mean can be greatly affected by outliers or extreme values.

5. Can the mean be used with all types of data?

No, the mean can only be used with numerical data. Categorical data, such as gender or eye color, cannot be used to calculate the mean because they do not have numerical values. In addition, the mean should not be used with skewed data, as it may not accurately represent the central tendency of the data.

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