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The arithmetic mean and the weighted mean are used in different situations. The arithmetic mean is used in frequencies as a general average. The weighted mean is used when different factors contribute to some kind of total for example with weighted index numbers.
It is not a matter of accuracy it involves using the right mean in the right situation. Almost always (if not always) a question will specify which mean to use.
What else can I help you with?
Can a variable measured at the interval or ratio level can have more than one arithmetic mean?
A variable measured at the interval or ratio level can have more than one arithmetic mean.
What is the sum of all the results included in the sample divided by the number of observation?
Mean or more precisely Arithmetic Mean
Is the mean or median more accurate?
None of them is "more accurate". They are answers to two different questions.
What is more accurate mean or median?
Technically the mean is more accurate, but it is not always a true representation, when you have a number that is way out of proportion with the rest of the numbers. That is when the median is more useful. See the related question below.
The middle of a set of numbers found by dividing the sum of all the numbers by the number of numbers in the set?
"Average" or "Mean" or, more specifically, "Arithmetic Mean"
Explain the difference between arithmetic mean and weighted mean?
The plain arithmetic mean is actually a special case of the weighted mean, except all the weights are equal to 1. The arithmetic mean is the sum of all the individual observations divided by the number of observations. With a weighted mean you multiply each observation by a weight, add those values together and then divide by the sum of the weights. E.g. Let's say you have 3 observations: 4, 7, 12 The arithmetic mean is (4+7+12) / 3 = 23/3 = 7.67 Now let's assume that you want to weight the first observation by a factor of 10, the second observation by a factor of 5 and the third observation by a factor of 2: The weighted mean is (4x10+7x5+12x3) / (10+5+2) = 111/17 = 6.53 You can see that if all the weights were 1 you would have the arithmetic mean shown above. As it is mentioned above arithmetic mean is a special case of weighted mean. In the calculation of arithmetic mean all the observations are given an equal chance of occurance ie the above mentioned problem can be written as 4*1/3+7*1/3+12*1/3=7.67 or inother words 7.67 is the number it takes if all are given equal chance whereas in weighted mean the chance of occurance are not equal .This can be written as 4*10/17+7*5/17+12*2/17=6.53 in the above eg. 4 has given more weightage than 7 and 12 has the least weightage so the probability of 4 occurring is more when compared to 7 and 12 there fore the average obtained is seen to decrease as we have given more importance to 4 than others. It shows that the average is affected by the weightage given to the numbers
How do you get weighted mean?
A weighted mean is when some values contribute more than others. In order to calculate weighted mean multiply each weight by its value, add those and then divide by the sum of the weights.
What is arithmetic mean return?
The arithmetic mean is more commonly known as the average. It is the sum of the values divided by the number of values.
Can a variable measured at the interval or ratio level can have more than one arithmetic mean?
A variable measured at the interval or ratio level can have more than one arithmetic mean.
How weighted score does calculate?
A weighted average is a more accurate measurement of scores or investments that are of relative importance to each other. Identify the numbers to be used, identify the weights of each number, convert percentages to decimals, multiply each number by its weight, and add them together to get the weighted score.
Can a mean have more than one value?
There is one arithmetic mean and one geometric mean to a set of numbers.
How does a mathematic mean differ from an average?
Short answer: NoLong answer: There is, strictly speaking, no single "mathematic mean" but there is an Arithmetic Mean, a Geometric Mean and a Harmonic Mean (see the related linl for some more details)The "Arithmetic Mean" is what is generally considered the "Average"
What is the sum of all the results included in the sample divided by the number of observation?
Mean or more precisely Arithmetic Mean
What is a good time weighted return and how can it be calculated effectively?
A good time-weighted return is a measure of investment performance that eliminates the impact of cash flows. It is calculated by taking the geometric mean of a series of sub-period returns. This method is effective because it accounts for the timing and size of cash flows, providing a more accurate measure of investment performance over time.
Is the mean or median more accurate?
None of them is "more accurate". They are answers to two different questions.
What is the significance of weighted average uncertainty in statistical analysis and decision-making processes?
Weighted average uncertainty in statistical analysis is important because it allows for a more accurate representation of the variability in data. By assigning weights to different data points based on their reliability or importance, the weighted average uncertainty provides a more nuanced understanding of the overall uncertainty in the data. This is crucial in decision-making processes as it helps to make more informed and reliable decisions based on a more precise assessment of the data's reliability.
What is the purpose of the weighted mean?
Using a weighted mean is useful in situations where different population groups are contributing to an overall average, and you want to assign more influence to one group or the other based on a certain criteria. An arithmetic mean is a special case of the weighted mean where all the weights are equal. For example, let's say Population A of 2000 people has an average IQ of 140 and Population B of 100 people has an IQ of 90. You've been asked to determine the average IQ of the combined populations. Of course the correct thing to do would be to re-average all the combined individual scores, but let's say due to privacy reasons you don't have access to this information. The arithmetic mean of the two populations is (140+90)/2=115. However, Population A is much larger and contributes significantly more to the overall average, so you decide to weight based on population size. The weighted mean is (140*2000+90*100)/(2000+100) = 138, much closer to Population A's IQ. This is a fairer estimate of the overall average considering the relative population sizes. Weights are largely arbitrary, they don't always have to be based on population size alone. Let's say you have 5 reviewers of a product giving their overall satisfaction rating. The scores are 9, 7, 6, 7, 3. However you have a very high regard for Reviewer 1 so you assign her a weight of 15 (and the others remain at weight=1). The average score is 9+7+6+7+3/5=6.4 The weighted average score is 15*9+7+6+7+3/(15+4)=8.3 The weighted average is much closer to Review 1's opinion due to your weighting decision.
