exst 2201 lesson 2.3
Variance (σ2) is what type of measure of spread?
A measure of spread standardized for the number of data values.
The sum of squares (SS) is what type of measure of spread?
A raw measure of spread.
The mean (µ) is used when thinking about the data values in a column of data because? (select two of the answers below)
A single number is easy to think about. The mean best represents the values in the column of data.
Two data sets have the same size, but Data set A has a sum of squares of 97 and Data set B has a sum of squares of 197. In which data set are the data values more widely spread out?
Data set B, because a sum of squares of 197 is bigger than a sum of squares of 97.
How is the sum of squares (SS) standardized into variance (σ2)?
Divide by the degrees of freedom.
Match the appropriate set of statistics to the descriptions below.
Extract the most information from a column of data.-Efficient statistics. Less affected by extreme values.-Resistant statistics.
Match the appropriate statistic for a distribution of efficient statistics.
Mean- location Standard deviation- Spread Histogram- shape
Is the average deviation better than the standard deviation (σ)?
No, because the average deviation always equals zero.
A data value close to the mean has a?
Small deviation.
A bigger standard deviation for a data set means the data values are?
Spread wider apart.
To calculate variance, statistics does not average the deviations, instead it averages the?
Squared deviations.
The efficient measure of spread for a column of data is the?
Standard deviation.
What is the statistical term for all the squared deviations added together?
Sum of squares.
What information about a data value is given by its deviation?
The mathematical distance and direction from the mean.
Does the average deviation always equal zero for every data set?
Yes, because the positive and negative deviation cancel each other.
Does the sum of squares (SS) usually get bigger as more data values are added to the data set?
Yes, because there are more numbers in the data set to sum.
Can the standard deviation (σ) be used to find probability?
Yes, it can with a normal curve.
A deviation can never equal zero.
false
The mean (µ) is NOT needed to calculate a deviation.
false
A data value less than the mean has a?
negative deviation
In statistics, a deviation applies to only one data value.
true
What is the appropriate denotation for standard deviation?
σ for population, s for sample.
What is the appropriate denotation for variance?
σ2 for population, s2 for sample
Which one of the following answers is NOT correct about standard deviation?
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛=𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒2
What is the formula for the sum of squares (SS)?
𝑆𝑢𝑚𝑜𝑓𝑠𝑞𝑢𝑎𝑟𝑒𝑠=∑(𝑥−𝑥𝑏𝑎𝑟)2
