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Steph S.

What is the goal of descriptive statistics?

• To simplify large groups of data

What are the two processes we use to achieve this goal?

• Organization

o Examples: tables and graphs

o Allows us to determine the shape of the distribution (chpt 2)

• Summarization

o Summarizing the entire data set with just one number

o Allows us to determine central tendencies (chpt 3) and variability (chpt 4)

o Examples: tables and graphs

o Allows us to determine the shape of the distribution (chpt 2)

• Summarization

o Summarizing the entire data set with just one number

o Allows us to determine central tendencies (chpt 3) and variability (chpt 4)

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We can describe any distribution by using three pieces of information. Name each of these three pieces of information and explain exactly what each is describing?

• Shape:

o Tells whether the distribution is symmetrical or skewed

• Measurement of central tendency:

o One number that summarizes all the measurements of the scores

• Measurement of variability:

o One number that identifies whether the distribution is spread apart or clustered together

o Tells whether the distribution is symmetrical or skewed

• Measurement of central tendency:

o One number that summarizes all the measurements of the scores

• Measurement of variability:

o One number that identifies whether the distribution is spread apart or clustered together

What two things do deviations scores tell us about an individual score?

• Distance and direction from the mean.

Define standard deviation.

• The average of the deviation scores (the differences

between raw scores and the mean)

between raw scores and the mean)

How is variance the same as standard deviation?

• They both tell us the average distance of scores from the mean.

How is variance different from standard deviation?

• Variance is measured in squared scores and standard deviation is measured on the same scale as the data set was originally.

If you wanted to describe the amount of variability that exists in a sample in the way that is easiest to understand, should you use the variance or standard deviation? Explain your answer.

• You would want to use standard deviation because it is measured on the same scale as the data set instead of squared scores like the variance.

Why do we need to used different formulas for the variance of a population and for the variance of a sample?

• We need to use different formulas because the sample always underestimates the variability of the population.

Describe exactly how these formulas are different from one another?

• They differ by using degrees of freedom

• σ^{2}=SS/N and s^{2}=SS/(n-1)

• σ

how does a skewed distribution differ from a symmetrical distribution?

• A skewed distribution has the bulk of the data on one side of the graph revealing one visible tail.

• A symmetrical distribution has the bulk of the data in the middle and two tails.

• A symmetrical distribution has the bulk of the data in the middle and two tails.

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How does a normal distribution differ from a symmetrical distribution?

• A normal distribution is perfectly symmetrical, this makes it predictable.

• Symmetrical distribution may not be predictable, may have no body, or two bodies

• Symmetrical distribution may not be predictable, may have no body, or two bodies

Explain the difference between tails and the body in a normal distribution. Which consists of the scores considered extreme?

• the body is where the typical scores are usually found

• tails are where the extreme scores are usually found.

• Tail is considered extreme

• tails are where the extreme scores are usually found.

• Tail is considered extreme

determine the average of the squared deviation scores

- Variance

determine the average score of variable measured on a nominal scale

- mode

determine the most frequently occurring score in a sample

- mode

determine the average score of a skewed distribution

- median

graph sample data measured on a discrete scale

- bar graph

determine how far away from the mean an individual score is

- standard deviation

Determine, on average, how far away from the mean we would expect to see any score

- standard deviation

Graph sample data from a quantitative variable

- histogram

Determine the average score to be used in inferential statistics

- mean

M

- mean of sample

σ

- standard deviation of a population

n

- number of scores in a sample

μ

- means of a population

σ^{2}

- variance of a population

s

- standard deviation of a sample

x

- means of a sample

s^{2}

- Variance of a sample

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