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Describing Numerical Variables

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Describing Numerical Variables

Examining each numerical variable in your analysis

- Variables measured with meaningful numerical values.
- Ratio
- True zero (ex., weight, height, age)

- Interval
- equal interval between values but no true zero point (ex., sociological or psychological scales)

- Discrete
- Values can only take whole numbers as values

- Continuous
- Values have no real breaking point
- Have infinite number of possible values

- Ratio

- Measures of Central Tendency
- Mean – the arithmetic average
- Mode – the most popular/common value of response
- Median – the value at which 50% of the cases lie above or below

- Measures of Dispersion
- Range – the distance between the highest and lowest value in the variable. Include minimum and maximum value of variable.
- Variance – how much values for a variable vary from the mean. Sum of the squared deviations from the mean
- Standard Deviation – the square root of the variance is typically used to evaluate the dispersion of cases around the mean.
- Skewness – how evenly/symmetrically the cases are distributed around the mean.

- Calculate the range.
- Order all of the cases for your numerical data from hi to low values. Take the maximum value and subtract from it the minimum value. The result is the range.

- Calculate the mean.
- Sum together the values for all cases and then divide by the total number of cases ((xi – X)/n)

- Calculate the median
- Ordered cases from high to low. It is the point value where half the cases lie above and half below it.

- Calculate the mode.
- Ordered cases from high to low, select the most common value.

- Calculate the variance
- For each case, take the value and subtract the mean from it. Take this result and square it. Take and sum the squared deviations for all cases of the variable. Divide the result by the number of cases. ((xi – X))2/n)

- Calculate the standard deviation
- The square root of the variance

- Create a histogram
- A graph which plots the frequency for values of the variable. The x axis is the value of the values for the variable. The y axis is the total number of cases.

Examine each variable for skewness,

- case distributions across values
- outliers
- decide if need to recode any variable
- Decide which measure of central tendency best describes your variable. Means are not very useful for skewed distributions.

- Arrange cases fro hi to lo values.
- Find the minimum value
- 18

- Find the maximum value
- 65

- Subtract the maximum from the minimum.
- 65-18 = 47

- Sum all values for all cases
- 18+20+21+30+32+36+45+52+60+65 = 379

- Divide by the total number of valid cases
- 379/10 = 37.9

- What is it the mode?
- What is the median?
- 32+36=68/2=34

- Subtract the mean from the value
- Square the result
- Sum the squared deviation
- 396.01+320.41+285.61+
- 62.41+31.36+36.1+50.41+
- 198.81+488.41+734.41=
- 2603.94
- Divide the result by the total number of cases
- 2603.94/10=260.394

S = 16.14

- Follow along the exercise in Assignment 2 of Ready, Set, GO Text.
- Use the Frequency procedure
- Get frequencies for all of your categorical variables
- Get range, mean, median, mode,standard deviation and variance

- Use the Charts command to get histograms for all of your variables
- Discuss results for each variable – spread, skewness, best measure of central tendency, frequency distribution
- Turn in by next Tuesday.
- This will be the first part of the results for Project 2.