Descriptive statistics- mathematical methods for ...
Descriptive statistics- mathematical methods for summarizing sets of data (raw scores)
Normal distributions- symmetrical, bell-shaped curve (most scores fall near average/few fall near extremes)
Positively skewed distribution = mean is higher than the median (more low scores than high)
Negatively skewed distribution = mean is lower than the median (more high scores than low)
Central tendency- center or middle distribution of scores computed as…
Mode- most frequently occurring score
Median- middle score
Mean- average score
Variability- (shows diversity of the distribution) the degree to which scores
are clustered around the middle of the distribution measured by…
[pic]
Range- difference between the highest and lowest scores
Standard deviation- the average of the differences between individual scores and the mean
(average distance from the mean)
a. calculate the difference between each score and the mean
b. square those differences
c. calculate the mean of the squares of differences = the variance
d. take the square root of those means = the standard deviation
☺or just use your scientific calculator…
Standard Deviation = square root of the variance
Variance = square of the standard deviation
[pic]
Let’s practice….
Which of the following series has the greatest range?
a. -2, -1, 0, 1, 2
b. -5, -3, 3, 5
c. -10, -5, 0, 5, 10
What is the _____ of the following distribution: 6, 2, 9, 4, 7, 3
a. mean? b. median? c. mode?
Walter gets a perfect 100 on a test that everyone else fails. If we were to graph this distribution, it would be …
If the variance is 100, the standard deviation would be…
If the variance is 64, the standard deviation would be…
If the standard deviation is 5, the variance would be…
If the standard deviation is 11, the variance would be…
Z scores measure the difference of a score from the mean in units of standard deviation. Scores below the mean have a negative Z score and those above have a positive Z score.
If Ramon scored 100 on a test with a standard deviation of 10 and a mean of 80, his Z score would be…
100 – 80 = 20/10 = +2
If Clara scored a 72 on a test with a mean of 80 and a standard deviation of 8, her Z score would be…
Tammy scored a 145 on an IQ test with a mean of 100 and a standard deviation of 15, her Z score would be…
What about figuring percentages?
For a test with normally distributed scores, the mean was 70 and the standard deviation was 10. Approximately what percentage of test takers scored 60 and above?
In a normal distribution, 50% (½) will score
above or below the mean. In a normal
distribution, 34% will score within one
standard deviation below the mean.
(70 - 60 = 10/10 = 1 SD)
50% (½) + 34% (1 SD) = 84%
For a test with normally distributed scores, the
mean was 80 and the standard deviation was 2.
Approximately what percentage of test takers
made a 76 and above?
(80 - 76 = 4/2 = 2 SD)
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Few Tips:
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• There can be more than 1 mode (2 = bimodal)
5
8
9 6.6 mean
4
7
b
c
d
a...
68% = 1 SD 95% = 2 SD 99% = 3 SD
34.1 + 34.1 68 + 13.6 + 13.6 95 + 2.1 + 2.1
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