Which measure of central tendency is obtained by adding up all of the scores and then dividing by the total number of scores quizlet?

If you change even one value of one score, this changes the mean because it first changes sum of x.

If you add or remove a score, it usually changes the mean, but not always. The exception is when the new or removed score is the exact same value as the mean before the change. Think of this score as sitting right on top of the fulcrum under the see-saw. It won't change the balance.

Also, if you increase or decrease each score by the same amount, it will have the exact same effect on the mean, either increasing or decreasing it by the same amount.
Ex: If you "added" a treatment to a sample group that changes each participant's pretreatment score by 2 points, it would change the new mean by two points in the same direction.

When multiplying or dividing each score by a constant as well, the same thing goes for the mean as it does when adding or subtracting the same from each score.
Ex: If you measure using inches, and you want to convert those scores to feet, you divide by 12. So the mean would change in the same way. Just remember that the measurement is still the same, even if you report it in inches vs. feet vs. cm, etc.

Four reasons to use the median vs. the mean. In the first three cases, we are dealing with numerical data (where the mean is usually preferred). I.e. interval or ratio scales of measurement. The fourth reason involves ordinal data.

In all cases, either the mean cannot be calculated, or the calculation of a mean produces a value that is not central or not representative.

1. When the distribution contains outliers or is skewed. The median is not usually affected by extreme scores. Ex. would be average income. Extremely wealthy people's incomes are outliers and do not represent the majority, so with income averages, the median is preferred.

2. If there is an undetermined score in the distribution. If, for ex., a participant never completed the assigned experimental task. This participant still represents the population, and their score should still be included, but a mean cannot be calculated with their score.

3. If there is no upper or lower limit to a category in a distribution, the distribution is considered open-ended. For ex., if a study examined how many pizzas a person in a sample of students could eat, and one of the categories was "5 or more," that isn't a measurable score.

4. Ordinal scale data. Mean measured distance (remember the see-saw, where the scores on each side of the fulcrum equal the same amount of total DISTANCE). But ordinal scales don't tell you distance, only order. So the mean doesn't work.

The score that has the greatest frequency. In common usage, the term means "a popular style" so it represents the most common score in a distribution. The definition of the mode is the same for a sample as it is for the population.

There are no symbols or notation for the mode, and no symbol to differentiate the sample mode from the population mode.

The mode can be used for analyzing any scale of measurement, including nominal scales (e.g. what your favorite ice-cream is if the ice cream flavors were coded with a number). The mode is the only average usable with nominal data (and also with discrete data).

The mode also shows an actual score in the distribution because its the most frequent score, whereas the mean and median are often calculated values that are not actual scores in the distribution.

Remember that the mode may not always be at the center of the distribution. Its just what is most frequent.

Three main reasons to use the mode:
1. Nominal data. These data don't tell you anything about value or distance, just name differentiation. So you can't use a mean or median.
2. Discrete variables. Even though you can use a mean when discrete variables produce a numerical score (when they don't, you can't calculate a mean), the mode is still the better measure of central tendency. For ex., you can calculate the mean number of children in an American household as 2.4, but people would rather hear a whole number given for discrete variables. So the mode would be better.

Often the mode is included in text to show the overall shape of the distribution. The mode shows the peak(s) in the distribution, so it helps give a visual of the data.

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Which measure of central tendency is the score that divides the distribution into two equal parts so that half of the cases are above and half are below it quizlet?

Which measure of central tendency is the score that divides the distribution into two equal parts?

Which measure of central tendency is the score that divides the distribution into two equal parts so that half of the cases are above and half are below it?

Which measure of central tendency exactly balances all of the scores?