# Diff in mean and median relationship

### Difference Between Mean and Median (with Conmparison Chart) - Key Differences Explains how to compute the mean, median, mode, and range of a list of The " range" of a list a numbers is just the difference between the largest and smallest. In a perfectly symmetrical, non-skewed distribution the mean, median and mode As distributions become more skewed the difference between these different. Here at zolyblog.info we're no math experts, words are our game. But, with some help from our friends at zolyblog.info and their super-easy-to-understand.

Mean Median Mode relationship in Symmetric distribution For a symmetrical distribution, all the three measures of central tendency are equal i.

### Central Tendency (Mean, Median, Mode) - StatsDirect

Imagine a situation in which the symmetrical distribution is made asymmetrical or positively or negatively skewed by adding some observations of very high or very low magnitudes, so that the right hand or the left hand tail of the frequency curve gets elongated. Consequently, the three measures will depart from each other.

Since mean takes into account the magnitudes of observations, it would be highly affected.

DIFFERENCE BETWEEN MEAN AND MEDIAN WITH EXAMPLES_STATISTICS_LESSON 1

Further, since the total number of observations will also increase, the median would also be affected but to a lesser extent than mean. Finally, there would be no change in the position of mode. Empirical Relationship between Mean, Median and Mode Empirical Relation between Mean, Median and Mode Empirically, it has been observed that for a moderately skewed distribution, the difference between mean and mode is approximately three times the difference between mean and median, i.

• What the difference between mean and median tells us about income inequality
• Difference Between Mean and Median

The mean and median of a moderately skewed distribution are Find mode of the distribution. For a moderately skewed distribution, the median price of men's shoes is Rs and modal price is Rs Calculate mean price of shoes.

Choice of a Suitable Average The choice of a suitable average, for a given set of data, depends upon a number of considerations which can be classified into the following broad categories: Considerations based on the suitability of the data for an average.

Considerations based on the purpose of investigation.

### What the difference between mean and median tells us about income inequality | Chartable

Considerations based on various merits of an average. The nature of the given data may itself indicate the type of average that could be selected. For example, the calculation of mean or median is not possible if the characteristic is neither measurable nor can be arranged in certain order of its intensity.

However, it is possible to calculate mode in such cases.

## Means and medians of different distributions

Suppose that the distribution of votes polled by five candidates of a particular constituency are given as below: Since the above characteristic, i. However, the mode of the distribution is D and hence, it can be taken as the representative of the above distribution.

If the characteristic is not measurable but various items of the distribution can be arranged in order of intensity of the characteristics, it is possible to locate median in addition to mode. For example, students of a class can be classified into four categories as poor, intelligent, very intelligent and most intelligent. Here the characteristic, intelligence, is not measurable.

However, the data can be arranged in ascending or descending order of intelligence.

## RELATION BETWEEN MEAN, MEDIAN AND MODE Quantitative Techniques for management

It is not possible to calculate mean in this case. If the characteristic is measurable but class intervals are open at one or both ends of the distribution, it is possible to calculate median and mode but not a satisfactory value of mean.

However, an approximate value of mean can also be computed by making certain an assumption about the width of class es having open ends. If the distribution is skewed, the median may represent the data more appropriately than mean and mode. If various class intervals are of unequal width, mean and median can be satisfactorily calculated. However, an approximate value of mode can be calculated by making class intervals of equal width under the assumption that observations in a class are uniformly distributed.

The accuracy of the computed mode will depend upon the validity of this assumption. The choice of an appropriate measure of central tendency also depends upon the purpose of investigation. If the collected data are the figures of income of the people of a particular region and our purpose is to estimate the average income of the people of that region, computation of mean will be most appropriate. On the other hand, if it is desired to study the pattern of income distribution, the computation of median, quartiles or percentiles, etc. Similarly, by calculating quartiles or percentiles, it is possible to know the percentage of people having at least a given level of income or the percentage of people having income between any two limits, etc.

If the purpose of investigation is to determine the most common or modal size of the distribution, mode is to be computed, e. The middle value is still going to be the same middle value, you can move this anywhere around in this range it's not going to change the median. But the mean will change, if this becomes really, really astronomically high it will distort the actual mean here, actually could distort it a good bit.

So for geology majors from UNC the median income is going to be lower than the mean because Michael Jordan is pulling the mean up. So let me fill that in. They all took the exact same job at the same company earning the same salary. So let's say all 3 of them earn 50 thousand dollars. That would be the mean. If you wanted the median you list the salaries in order and then you take the middle one, well the middle one is 50, so in this case the median is equal to the mean.

So let's fill that in, median is equal to the mean. And then finally, wait let me go back to my scratchpad. Whoops, let me go back to my scratchpad here. So here we have 35, out of the 35, 32 got high-paying consulting jobs so let's say that they were making six-figures so the distribution might look something like this, this is 0 and this is let's say this is 50K and let's say that this right over here is thousand dollars a years.

So 32 got high-paying consulting jobs, so you might have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, So the distribution for the people who got the jobs might look something like that but there were 3 people who are unemployed so let's say they got no income, so you have 1, 2, 3.

So this is now, you have 3 outliers like the Michael Jordan situation but instead of them being very high they are very low so they're going to pull the mean lower, they're not going to, if these were 0 or these were 50, or these were over here, they're not going to affect the median. The middle number is still going to be the same. But they are going to pull down the mean. So here I would say that the median income will likely be higher, will likely be greater than the mean. 