Standard Deviation and Variance

The video tutorial covers measures of dispersion, focusing on variance and standard deviation. It explains how variance is calculated by squaring deviations and taking their mean, and how standard deviation is the square root of variance. The tutorial discusses the properties of standard deviation, its applications in various fields, and methods to compute it for grouped data. Examples illustrate the concepts, highlighting the importance of standard deviation in comparing data sets and assessing variability.

Which measure of dispersion is used to calculate the spread of data by considering the absolute deviations from the mean?

• Mean Deviation

• Variance

• Quartile Deviation

• Range

What is the main advantage of using variance over mean deviation?

• Variance considers the direction of deviations

• Variance is easier to calculate

• Variance is always smaller than mean deviation

• Variance uses absolute values

Who introduced the term 'variance'?

• Sir Ronald Fisher

• Karl Pearson

• Francis Galton

• John Tukey

What does a higher standard deviation indicate about a data set?

• Greater variability

• Less variability

• Data points are closer to the mean

• Greater consistency

In the context of investments, why might an investor choose a stock with a lower standard deviation?

• It means the stock is undervalued

• It indicates higher returns

• It shows greater volatility

• It suggests lower risk

What happens to the standard deviation if a constant is added to each observation in a data set?

• It increases by the constant

• It decreases by the constant

• It remains unchanged

• It doubles

If each observation in a data set is multiplied by a constant, how does the standard deviation change?

• It is multiplied by the constant

• It is divided by the constant

• It is squared

• It remains the same

Which method of computing standard deviation for grouped data involves using an assumed mean?

• Direct method

• Shortcut method

• Assumed mean method

• Step deviation method

What is the first step in the step deviation method for computing standard deviation?

• Compute the deviation of each observation

• Choose an assumed mean

• Identify the midpoint for each class

• Calculate the variance

Which method of computing standard deviation is known for simplifying calculations by using both properties of standard deviation?

• Direct method

• Assumed mean method

• Step deviation method

• None of the above