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正文1

Research Methods: Statistics

• Descriptive statistics describes a set of data.
  • How many people have black hair in this room?
  • How many people play a musical instrument?

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• Measures of Central Tendency describe the center of a data set.
• The measures of central tendency are the Mean, Median, and Mode.

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• The Mean or average is the sum of scores divided by the number of scores.
  • Sum of scores / Number of days = Mean
• "Find the mean of coffee consumption per day."
  • Day 1: 1
  • Day 2: 4
  • Day 3: 5
  • Day 4: 2
  • Day 5: 3
• Sum the scores:
  • 1+4+5+2+3=15
• Divide the score by the number of days:
  • 15/5=3
• "Mean or average is 3 cups / day"

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Median is at the midpoint of a frequency distribution, such that there is an equal probability of falling above or below it

• How to find the Median: Put all the numbers in numerical order.
  • If there is an odd number of scores, the median is the middle number.
  • If there is an even number of scores, the median will be the mean of the two central numbers.

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• "What is the median?"
  • 6, 2, 9, 4, 7, 3
• Rearrange the numbers:
  • 2, 3, 4, 6, 7, 9
• If there is an even number, find mean of middle two:
  • 4+6=10. 10/2=5. Five is the median.

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• The mean is prone to problems with outliers. Outliers are extreme scores that skew the mean. The median is sometimes a better measure of central tendency when there are outliers.
  • • Salaries in a company:
    • Employee 1: $35,000
    • Employee 2: $45,000
    • Employee 3: $43, 000
    • Employee 4: $400,000
  • Mean: $130,750
  • Median: $44,000

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• The mode is the score that appears most frequently in a set of numbers.
  • 4, 5, 6, 7, 7, 7, 7, 8, 5, 5, 6, 6, 8, 3, 2, 4, 4
  • What is the mode? 7
• There may be no mode if no value appears more than any other.
• There may also be two modes (bimodal), three modes (trimodal), or four or more modes (multimodal).

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Normal Distribution

• A Normal distribution' is a function that represents the distribution of many random variables as a symmetrical bell-shaped graph.
• Measures of Central Tendency are a part of a normal distribution.
• The mean, median, and mode of a Standard Normal Distribution are 0

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• Normal Distribution, Measures of Central Tendency, and Skew.jpg

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• Positively skewed means that a distribution of scores includes an extreme score(s), which give the graph a long tail trailing to the right.
• A negatively skewed distribution contains more high scores than low scores, but a few really low scores result in the graph having a 'long tail' to the left.

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正文2

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