# Questions tagged [central-tendency]

In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages.The tendency for the values of a random variable to cluster round its mean, mode, or median.

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### Why is it assumed that the mode, in a grouped frequency distribution, lies in the modal class(the class with maximum frequency)?

I am in 10th standard. We are given a formula to find the mode mode = l +[(f1-f0)/(2f1-f0-f2)]h Where l is the lower limit, F1 the modal class i.e the class with most frequencies, f0 the frequency of ...
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### Where I am confusing about the concept of 'weightage' and 'Balance Point'?

By Balance point I understand equal weight on both sides of a lever. Various sources, including stackexchange threads use to treat 'mean' as 'balancing point'. We want to place a fulcrum on the line ...
133 views

### Why are mean, median, and mode called central tendency?

Is there any difference between the two terms "Central tendency" and "representative values"? Why are mean, median, and mode called central tendency or representative values?
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### Why is the mode a measure of central tendency?

Is mode a measure of central tendency just because it's the most frequent? Is it enough to say that it's in the center? I think it's lame, and there might be some other reason why we call it a measure ...
255 views

### No mode or all mode?

Let's say I have a data set:- $${1,2,3,4,5}$$ I decide to find the mode though it would not be an appropriate measure of central tendency. But still........ Now this is an exceptional case and for ...
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1 vote
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### Determine variance of item level scores within single test and sample of tests

I am decades out of school and need help determining the correct statistic / concept to use for my use case. My agency (human services) uses a specific functional test to determine how well clients ...
311 views

### Mid-range via minimax

Warning: crossposted at Statistics SE. Given vector ${\rm a} \in \Bbb R^n$, \begin{array}{ll} \displaystyle\arg\min_{x \in {\Bbb R}} & \left\| x {\Bbb 1}_n - {\rm a} \right\|_2^2\end{array} = \...
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1 vote
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### Is there a non-mathematical definition of the geometric mean?

I am aware that the geometric mean is often used with the lognormal distribution, because then it directly relates to the arithmetic mean with the normal distribution. But I was trying to think of an ...
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### Measure of Central Tendancy - Modal Class Identification

I have been studying Measure of Central Tendency where we need find Mean, Median and Mode I have problems finding the modal class in Mode calculation. I would like ...
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### If variance is $\mathrm E[(X-\mu)^2]$, then what is $\mathrm E[X-\mu]$?

The question is pretty straightforward. The variance of a random variable $X$ with mean $\mu$ is defined as $\mathrm E[(X-\mu)^2]$ and is notated $\operatorname{Var}(X)$ or $\sigma^2$. Another ...
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### Not able to solve it for n>2 observations

The relation between $\textrm{AM, GM , HM}$ is given as follows $AM \times HM=( GM )^2$ Does it also follow if the number of observations are more than $2$?
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### Mean changing with changing frequencies and class intervals

Let $A$ denotes weekly wages and $B$ denotes Number of workers. \begin{array} {|r|r|}\hline A & 50-55 & 55-60 & 60-65 & 65-70 & 70-75 & 75-80 & 80-85 & 85-90 \\ \hline ...
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### should I use the mean or weighted mean in this example?

An investor calculated the percentages of each of three stock investments with payoffs as shown. Find the average payoff for the three stock investments. what should I use in this case to calculate ...
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### How do I find the expected return on a ticket?

A lottery has a grand prize of 400,000 dollars, five runner up prizes of 50,000 dollars each, nine third-place prizes of 10000 dollars each, and twenty-five consolation prizes of 1000 dollars each. If ...
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Does central tendency necessarily have to lie between the two numbers?For eg. I understand $2,4,8$ are in GP with $4$ being the GM of $2,4,8$. But what about $2,-4,8$ if we consider common ratio to ...