Selecting a measure of central tendency The mean, median, and mode are all measu

Question

Selecting a measure of central tendency The mean, median, and mode are all measures of central tendency. The mean is usually the preferred measure of central tendency, but there are specific situations in which it is impossible to compute a mean or in which the mean is not particularly representative of the distribution. Which of the following statements about the mean are true? Check all that apply. It always corresponds to an actual score in the data. It can be used for data that are measured on a nominal scale. It is commonly referred to as the arithmetic average. It is algebraically defined (that is, there is an equation you can use to calculate its value). Which of the following statements about the median are true? Check all that apply. It is appropriate for ordinal data. It is algebraically defined (that is, there is an equation you can use to calculate its value). It is not easily affected by extreme scores. There can be more than one. Which of the following statements about the mode are true? Check al that apply. It is the score at the 50^th percentile. It corresponds to an actual score in the data. It is also referred to as the arithmetic average. There can be more than one.

Explanation / Answer

1) The answer is "c" it 's commonly referred as a arithmetic average why because

the most commonly used and readily understood measure of central tendency. In statistics, the term average refers to any of the measures of central tendency. The arithmetic mean is defined as being equal to the sum of the numerical values of each and every observation divided by the total number of observations.

2) The answer is "a" it's appropriate for ordinal data.

have been reading about appropriate measures of central tendency for ordinal level data. So far I have learned that the median and mode can be used but that the latter can only be used in some cases. Some sources state that the median can only be used with Likert questions when there is an odd number of scores. It is not clear to me what this means and also which cases the median cannot be used.

Median is the value which occupies the middle position when all the observations are arranged in an ascending/descending order. It divides the frequency distribution exactly into two halves. Fifty percent of observations in a distribution have scores at or below the median. Hence median is the 50th percentile.Median is also known as ‘positional average’.[3]

It is easy to calculate the median. If the number of observations are odd, then (n + 1)/2th observation (in the ordered set) is the median. When the total number of observations are even, it is given by the mean of n/2th and (n/2 + 1)th observation.

3) The answer is "D" there can be more than one.

Mode is defined as the value that occurs most frequently in the data. Some data sets do not have a mode because each value occurs only once. On the other hand, some data sets can have more than one mode. This happens when the data set has two or more values of equal frequency which is greater than that of any other value. Mode is rarely used as a summary statistic except to describe a bimodal distribution. In a bimodal distribution, the taller peak is called the major mode and the shorter one is the minor mode.

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