What is the best measure of central tendency to represent the number of children in a household?
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If you change even one value of one score, this changes the mean because it first changes sum of x. Show 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. 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. 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: 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. Measures of central tendency are numbers that describe what is average or typical within a distribution of data. There are three main measures of central tendency: mean, median, and mode. While they are all measures of central tendency, each is calculated differently and measures something different from the others. The MeanThe mean is the most common measure of central tendency used by researchers and people in all kinds of professions. It is the measure of central tendency that is also referred to as the average. A researcher can use the mean to describe the data distribution of variables measured as intervals or ratios. These are variables that include numerically corresponding categories or ranges (like race, class, gender, or level of education), as well as variables measured numerically from a scale that begins with zero (like household income or the number of children within a family). A mean is very easy to calculate. One simply has to add all the data values or "scores" and then divide this sum by the total number of scores in the distribution of data. For example, if five families have 0, 2, 2, 3, and 5 children respectively, the mean number of children is (0 + 2 + 2 + 3 + 5)/5 = 12/5 = 2.4. This means that the five households have an average of 2.4 children. The MedianThe median is the value at the middle of a distribution of data when those data are organized from the lowest to the highest value. This measure of central tendency can be calculated for variables that are measured with ordinal, interval or ratio scales. Calculating the median is also rather simple. Let’s suppose we have the following list of numbers: 5, 7, 10, 43, 2, 69, 31, 6, 22. First, we must arrange the numbers in order from lowest to highest. The result is this: 2, 5, 6, 7, 10, 22, 31, 43, 69. The median is 10 because it is the exact middle number. There are four numbers below 10 and four numbers above 10. If your data distribution has an even number of cases which means that there is no exact middle, you simply adjust the data range slightly in order to calculate the median. For example, if we add the number 87 to the end of our list of numbers above, we have 10 total numbers in our distribution, so there is no single middle number. In this case, one takes the average of the scores for the two middle numbers. In our new list, the two middle numbers are 10 and 22. So, we take the average of those two numbers: (10 + 22) /2 = 16. Our median is now 16. The ModeThe mode is the measure of central tendency that identifies the category or score that occurs the most frequently within the distribution of data. In other words, it is the most common score or the score that appears the highest number of times in a distribution. The mode can be calculated for any type of data, including those measured as nominal variables, or by name. For example, let’s say we are looking at pets owned by 100 families and the distribution looks like this: Animal Number of families that own it
The mode here is "dog" since more families own a dog than any other animal. Note that the mode is always expressed as the category or score, not the frequency of that score. For instance, in the above example, the mode is "dog," not 60, which is the number of times dog appears. Some distributions do not have a mode at all. This happens when each category has the same frequency. Other distributions might have more than one mode. For example, when a distribution has two scores or categories with the same highest frequency, it is often referred to as "bimodal." What is the best measure of central tendency for family size?The mean is the most frequently used measure of central tendency because it uses all values in the data set to give you an average. For data from skewed distributions, the median is better than the mean because it isn't influenced by extremely large values.
What is the most appropriate central tendency for age?Clearly median seems to be the statistic of choice when it comes to ages.
What is central tendency in statistics for kids?central tendency refers to the average of a data set. • measures of central tendency include. mean, median and mode.
What is the best measure of the central tendency of the sample data?The median is less affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical.
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