Post on 30-Dec-2015
Descriptive Statistics
• Just describes sets of data.
• You might create a frequency distribution.
• Frequency polygons or histograms.
Measures of Central Tendency• Mode – score that occurs most often
EX: 3,5,5,7,5,4,9,6,8,7,10 5 is the mode
• Median – score in the halfway point EX: 3,4,5,5,5,6,7,7,8,9,10 6 is the median
• Mean – average score EX: 3+5+5+7+5+4+9+6+8+7+10=69
69/11 6.27 is the mean
Mean, Median, Mode
• The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200.
– For these six salaries, find: •(a) the mean •(b) the median •(c) the mode
Mean, Median, Mode• AnswersMean: 90+ 140+ 140+ 180 + 200 + 220 =$ 161.67
6
Median: 90,140,140,180,200,220
The two numbers that fall in the middle need to be averaged.
140 + 180 = 160
2
Mode: 90,140,140,180,200,220
The number that appears the most is 140
Let’s say you are looking to move to a new place….
• The average income of a family in the new city is 70,000 – not too bad….
• However….• 26 families make less than 70,000• Only 3 families make more than
70,000
Skewed Distributions
15 20 25 30 35 40 45 50 90 475 710
70
Mode Median Mean
One Family Income per family in thousands of dollars
Distributions• Outliers skew
distributions.• If group has one
high score, the curve has a positive skew (contains more low scores)
• If a group has a low outlier, the curve has a negative skew (contains more high scores)
Measures of Variability• Range: distance
from highest to lowest scores.
• Standard Deviation: the variance of scores around the mean.
• The higher the variance or SD, the more spread out the distribution is.
• Do scientists want a big or small SD?
Calculating the Standard Deviation
1. Figure out the Mean: 16 4 = 42. Take mean & figure out difference
from each point: 2-4=-2, 2-4=-2, 4-4=0, 8-4=4
3. Square each difference:4,4,0,164. Add together: 4+4+0+16=245. Divide by #: 24 4 = 6 This is
the variance6. Take square root: 2.45
Data: 2,2,4,8
Normal Distribution
A standard deviation of 15 accounts for about 68% of responses.
A normal distribution is a bell shaped curve.