Question

The various quotient and Composite scores have a mean of ____ and a standard deviation of ___.:

Answer 1

The mean of the various quotient and composite scores is ___
`\[ \bar{X} = (\sum_(i=1)^(n) X_i)/(n) \]` and their standard deviation is ___
`\[ s = \sqrt{\frac{\sum_(i=1)^(n)(X_i - \bar{X})^2}{n}} \]`

Step-by-step explanation:

The mean
`(\(\bar{X}\))` is calculated by summing up all the individual scores and dividing by the total number of scores. The formula for mean is:

`\[ \bar{X} = (\sum_(i=1)^(n) X_i)/(n) \]`

where
`\(X_i\)`represents each individual score, and
`\(n\)` is the total number of scores. Once you have the sum of all the scores, dividing by \
`n\)` gives you the mean.

The standard deviation
`(\(s\))` is a measure of the amount of variation or dispersion in a set of values. It is calculated using the formula:

`\[ s = \sqrt{\frac{\sum_(i=1)^(n)(X_i - \bar{X})^2}{n}} \]`

This formula involves finding the squared differences between each individual score
`(\(X_i\)) and the mean (\(\bar{X}\))`, summing these squared differences, dividing by
`\(n\)`, and then taking the square root.

In the context of the question, the blanks in the final answer can be filled in with the specific numerical values obtained from the calculations based on the given data.

These statistical measures, mean and standard deviation, provide valuable insights into the central tendency and variability of the various quotient and composite scores.