6.
Which is the best measure of central tendency for the type of data below–the mean, the median, or the mode? Explain.
Hours of sleep each night
Median; there will be outliers
Range; there are no outliers
Mode; the data are non-numeric
Mean; the outliers are limited
its d, connections academy
BUT I NEED PROOF/BACKUP SO THAT MY PARENTS DON'T SAY ITS A
To support the answer, let's analyze each option mentioned:
a) Median: The median is the middle value of a set of data when it is arranged in ascending or descending order. In this case, using the median as a measure of central tendency for hours of sleep each night may be suitable because it is less affected by extreme values or outliers.
b) Range: The range gives the difference between the highest and lowest values in a dataset. However, it does not provide information about the central tendency of the data. It only indicates the spread of the data.
c) Mode: The mode refers to the value that appears most frequently in a dataset. Since the data given (hours of sleep each night) is non-numeric, calculating the mode does not make sense. Mode is mostly used with categorical or qualitative data, such as favorite color or preferred music genre.
d) Mean: The mean is the average value of a set of data, obtained by summing all the values and dividing by the number of values. While the mean is commonly used as a measure of central tendency, it may be influenced by outliers. If there are a few extreme values that are significantly different from the rest of the data, they can distort the mean.
So, based on the options provided, it seems that the median (option a) would be the best measure of central tendency for the type of data given (hours of sleep each night). The median is not as susceptible to outliers and is more representative of the typical amount of sleep.
You can use this reasoning and information to explain to your parents why the median would be the most appropriate measure.
To determine the best measure of central tendency for a given data set, it is important to consider the nature of the data and any potential outliers. Let's evaluate the options provided for the "Hours of sleep each night" data and provide a detailed explanation:
a) Median: The median is the middle value that separates the upper half from the lower half of a dataset when arranged in ascending order. The median is generally a good measure of central tendency when there are potential outliers in the data. In the case of "Hours of sleep each night," there might be outliers such as individuals who sleep significantly more or less than the majority. The median is less affected by outliers as it is the actual middle value rather than relying on the sum of all values.
b) Range: The range is the difference between the maximum and minimum values in a dataset. While the range can provide insight into the spread of the data, it is not a measure of central tendency. It does not directly represent the typical value in the data set.
c) Mode: The mode is the value that appears most frequently in a dataset. However, in the case of "Hours of sleep each night," the data is described as non-numeric. The mode is typically used for categorical or nominal data where values are not numerical. Therefore, the mode would not be the best measure of central tendency for this specific data set.
d) Mean: The mean, or average, is the sum of all values divided by the number of values. In this case, you mentioned that the outliers are limited. If there are only a few outliers that do not significantly affect the overall data distribution, the mean can provide an accurate representation of central tendency. It can be useful to obtain an overall average value.
Considering all the options and explanations, the best measure of central tendency for the "Hours of sleep each night" data would be the median, as it is less affected by outliers.
First of all, the range is not a measure of central tendency.
The mean acts as a fulcrum (balance point) for the distribution, therefore outliers on one side will draw the mean out to that side. In other words, the distribution is significantly skewed.
In a skewed distribution, the mean is biased toward the outliers, while the mode is biased in the opposite direction. Under these conditions, the median is the most central of the measures of central tendency, and I would say A.
If the outliers are equal on both sides, the mean will not be effected.
For non-numeric data, the mode is the only measure of central tendency that can be used. However, hours of sleep are numerical.
I don't know if the following will help.
http://drdavespsychologypage.homestead.com/Two___Two_____four.pdf