AP Psychology; Statistics

mean

the average of all values. Σx/2

median

The middle of a set of data. Arrange the values in ascending order and find the middle. Good because it will give you a genuine value that someone got. Ex: the median of the test scores was 88, but the actual mean was 86.73, which nobody got.

mode

The most recurring value. Ex: 2, 2, 6, 7, 7, 9, 2 = 2 is the mode.

central tendency

mean, median, mode.

What can go wrong with mean?

Bill Gates walks into a café, and now the mean income of everyone in their is in the billions. SKEWED VALUES.

What can go wrong with the median?

It doesn't accurately display the distribution of scores, think of the seesaw example the book gave. The median was in the middle, but that did not reflect the amount of people.

What can go wrong w/ mode?

it's just not good

Bell Curve

When there is a large enough sample, there will be a bell curve. i cant put images so just imagine a bell. A large amount of scores will fall in the middle, with descending gradients on both sides. The scores on the sides are extremes, anomalies.

Standard Deviation

How much a score deviates from the average (i think). KNOW: the first standard deviation is at 68%, meaning that 68% will fall into that category. That is near the top of the bell curve. Then 95% lower down, and not too far from the bottom is the third standard deviation, 97.7%.

Measures of Variation

standard deviation and range. if a question asks for this, do not respond with mean, median, or mode!!!!!

Range

The difference between the highest score and the lowest score. A form of variation, and can also be disrupted by a few very high scores.

Standard Deviation Formula

Probably not on test but just to be safe:
√Σ(x-m)^2 / √N

When is it reliable?

1. Representative samples!!! Representative Samples > Biased Samples.
2. Less Variability > More Variability (i believe this is referring to uncontrolled/untested variables, meaning make sure everything except the medicine, for example, is the same)
3. More Cases > Fewer.

What are the mean, median, and mode measures of?

Central Tendency

Mean of 5,6,6,7,8, and 16?

8

In a distribution of test scores, which measures of central tendency would be likely to be the most affected by a couple of extremely high score?

Mean. Remember Bill Gates

Statistical reasoning helps us generalize from a ______ to a ______

Sample; Population

When is it significant?

1. Reliable measures of the populations
2. Large differences

Statistical Significance

the difference observed is probably not due to chance variation b/w the samples.