Can I calculate variance based on these descriptive statistics?

[Mir]

Hi everyone! I am currently revising for a statistics exam and am struggling with one particular practice question. I have attached a screenshot of the info that was provided.

The practice exam question is as follows:

Which of the following cannot be determined from the table of descriptive statistics in the block introduction:
- variance
- number of observations
- range
- IQR (interquartile range)

Our teacher told us that IQR is the correct answer. I initially thought that we could calculate the IQR by using the data in the graph. But I now understand that the data in the graph does not constitute descriptive statistics.

My question is, however, how can I calculate the variance based on the descriptive statistics only (so without using the data in the graph)? I can only seem to find examples of how to calculate this by using the data set.

Thanks in advance for your help!
Mir

 

[Dason]

Do you know how you would calculate the standard deviation for a data set?

 

[Mir]

I would calculate the mean of the data set, then for each number in the data set I subtract the mean and square the result, then I calculate the mean of those squared differences, and finally I take the square root of that.

My question is if the variance can be calculated based only on the following data: sample size, minimum, maximum, mean and standard deviation. However, based on your question I am worried this is a silly question. If so, please excuse my ignorance, I am a stats beginner.

In my stats book it says: "The variance is calculated as the average squared deviation of each number from the mean of a data set." I therefore didn't think it was possible without using the data set, which is the question asked in the practice exam.

 

[Dason]

Compare how you calculate variance with how you calculate standard deviation. Is there a relationship?

 

[Mir]

Thank you, that of course answers the question!