With an odd number, the median is the middle score in theordered list.9A distribution can have more than one _____. Show Get answer to your question and much more For any distribution, you can be sure that at least oneindividual has a score equal to the _____. Get answer to your question and much more The most commonly used measure of central tendency is_____. Get answer to your question and much more A professor records the academic major for each student ina class of n = 40. What would be the best measure ofcentral tendency for these data? Get answer to your question and much more One item on a questionnaire asks students how many timesin a typical week they eat at a fast-food restaurant. Theresponse choices are (1) Never, (2) Once, (3) Twice, (4)Three or more times. What is the best measure of centraltendency for the data from this question? Get answer to your question and much more For a perfectly symmetrical distribution with µ = 30, what isthe value for the median? Get answer to your question and much more In a negatively skewed distribution of exam scores, Tomscored at the mean, Mary scored at the median, and Janescored at the mode. Who had the highest score? Get answer to your question and much more Jenna Lehmann Central tendency is a statistical measure; a single score to define the center of a distribution. It is also used to find the single score that is most typical or best represents the entire group. No single measure is always best for both purposes. There are three main types:
Here is a variety of videos to help you understand the concepts of these measures, finding the median using a histogram, and finding a missing value given the mean. There are properties that will change in the mean depending on how scores are modified. When every score has a number added to it, the mean also gets the same number added to it (ex. if the mean is 8 and every score within the distribution as a 3 added to is, the new mean will be 11). When all the numbers are multiplied by a something, the mean is also multiplied by that something (ex. if the mean is 2 and all the numbers in the distribution were multiplied by 3, the new mean would be 6). When only a few scores are greater or lower, the mean value follows with it but it needs to be recalculated. The following videos detail what happens to the mean and median when increasing the highest value, the impact that removing the lowest value has on the mean and median, and estimating means and medians when given a graph. Computing Central Tendency MeasuresComputing the mean: The mean is pretty straightforward. One should add up all the values and divide that sum by the number of values. For example, if I have a data set of 5 (2, 6, 3, 2, 2), I would add all the numbers up (15) and divide that by 5 to get a mean of 3. Computing the median: Calculating the median involves lining up all the scores from smallest to biggest. The middle one is the median. If there are an even amount of numbers, the average of the 2 middle numbers is considered the median. Remember that the purpose of a median is to divide the data in half. When working with a discrete frequency distribution, please refer to the first video below. When working with a grouped or continuous frequency distribution, there are extra steps. Please refer to the second video included below. Computing the mode: Mode is the most frequent number which comes up. Whatever shows up the most in your frequency table, that’s the mode. There may be more than one mode, so keep this in mind. Computing weighted means: Overall mean is the sum of all the scores of group one plus the sum of all the scores in group two. All of this is then divided by n1+n2. In some cases you’ll get something like “group 1 consists of 5 people with an average score of 10 and group 2 consists of 8 people with an average score of 7.” In this case you would multiply 5 and 10 and add that to 8 times 7. You would then divide that number by the total number of people to get the weighted mean. Here is a helpful video: Central Tendency and How they Relate to Distribution ShapeThe shape of a distribution can help you determine which measure of central tendency is greatest.
When to Use Each MeasureIn regards to the mean, no situation precludes it, but it shouldn’t be used when there are extreme scores, skewed distributions, undetermined values, open-ended distributions, ordinal scales, or nominal scales. With the median, it’s appropriate to use when there are extreme scores, skewed distributions, undetermined values, open-ended distributions, or ordinal scales. It is not to be used when there is a nominal scale. The mode is good to use with nominal scales, discrete variables, and in describing shape, but it shouldn’t be used with interval or ratio data, except to accompany the mean or median. This chapter was originally posted to the Math Support Center blog at the University of Baltimore on June 4, 2019. Does adding a new score to distribution change the mean?Changing an existing score: Because every score in a distribution influences the value of the mean, changing one score into another score will change the mean. Increasing the value of an existing score will increase the value of the mean. Decreasing the value of an existing score will decrease the value of the mean.
What will always change the value of the mean?Changing the value of a score in a distribution will always change the value of the mean.
Which of the following actions will change the value of the mean?The correct answer for the effect that always changes the mean is b. Changing the value of one score.
What will happen to the mean value if all the scores in the distribution increase by 5?It will remain the same.
The range of data is the difference between the value of the largest score and the smallest score. If 5 points are added to each value the difference will remain the same.
|