Question

In: Statistics and Probability

Assignment Directions Answer the following critical thinking questions in this forum. Feel free to copy the...

Assignment Directions

  1. Answer the following critical thinking questions in this forum. Feel free to copy the questions and paste into your reply so that you cover each one. Use complete sentences and proper statistical terminology in all posts.
  2. Read the instructors response to the questions.
  3. Read the answers of some of your peers.
  4. Reply to your own post with any corrections you may have for your initial responses.

Questions:

  1. When is it best to use the mode as a measure of center? Describe what type of data would lead you to choosing the mode over the mean or median. [1 sentence]
  2. If a set of numbers has a standard deviation of zero, what can you say about the numbers? [1 sentence]
  3. If a set of grades for a class has a large range and a small standard deviation, what can you say about the class? Include an interpretation that is specific to grades in a class. [2 sentences]
  4. Why is the median less affected by skewed data than the mean? [2 sentences]
  5. Is most data likely to be skewed or symmetric? There is no right or wrong here but discuss and take a side on the issue. [2 sentences]

Solutions

Expert Solution

When is it best to use the mode as a measure of center?

When the data is nominal we use the mode as a measure of center. The mode is the number that repeats most often in a data set.

Describe what type of data would lead you to choosing the mode over the mean or median.

Type of Variable Best measure of central tendency
Nominal Mode
Ordinal Median
Interval/Ratio (not skewed) Mean
Interval/Ratio (skewed)

Median

All continuous data set has a median, mode and mean. However, the ordinal data set has a median and mode only, and nominal data has only a mode.

If a set of numbers has a standard deviation of zero, what can you say about the numbers?

When the standard deviation is zero, there is no spread; that is, all the data values are same.

If a set of grades for a class has a large range and a small standard deviation, what can you say about the class? Include an interpretation that is specific to grades in a class.

If most of the students have same grade and rarely one or two have low and high grade. Then the range will be larger but the standard deviation is lower. The data will be Normally distributed.

Why is the median less affected by skewed data than the mean?

Median is the middle observation of the data set. Where mean is the average of the observation. If there are extreme observations in the dataset then the middle observation is not affected by the extreme observation and the average will be affected by the extreme observation.

Is most data likely to be skewed or symmetric? There is no right or wrong here but discuss and take a side on the issue.

Most of the dataset are symmetric. Most of the observation in a data set has similar values. Rarely some have extreme values. Most of the data set normally distributed. Then it is symmetric.

orchestra answered 1 year ago
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