Statistics and Probability Terms | Mathematics

August 15, 2016 DRC Team

Statistics and Probability Terms | Mathematics

Will it rain today? Will traffic be heavy on the way to work? Will my boss be happy with my performance?

These are all questions of prediction. In a previous TASC Test Assessing Secondary Completion™ blog post on statistics and probability, we stated that every day you use probability when you make predictions and analyze for the best outcome.

Remember that:

  • Statistics is the study or practice of collecting and analyzing numerical data.
  • Probability is the likelihood of something happening.

Let’s review seven key terms that will help advance your understanding and study of statistics and probability:

  • A hypothesis is an educated guess/statement that can be tested.
    • Example: The more a student studies for the TASC test, the higher score his or her HSE score will be.
  • Independent events, A and B, are independent of each other if the fact that A occurs does not affect the probability of B occurring.
    • Example: Without looking, you choose a red pair of socks from your drawer (Event A). Then you put the red pair of socks back in your drawer. Without looking again, you choose a white pair of socks from your drawer (Event B).
  • The Mean is the average of a set of values. The mean is a calculated value. To find the mean of a set of numbers: Add up all of the numbers, then divide by how many numbers there are.
    • Example: Set of values {2, 4, 6, 8, 10}
      • Add up all of the values: 2+4+6+8+10 = 30.
      • Then, divide 30 by 5, since there is a total of 5 values in the set.
      • 30/5 = 6. 6 is the mean of this set of values.
  • The Median is the middle number in a set of values.
    • Example: Set of numbers {3, 13, 23, 33, 43}
      • The middle number in this set of values is 23.
    • Example: Set of numbers {19, 25, 31, 38, 46, 53}
      • This example has an even amount of values.
      • To find the median, take the two middle numbers – 31 and 38 – and add them together. 31+38 = 69.
      • Then, divide 69 by 2. 69/2 = 34.5 is the median of this set of values.
  • A sample size is a portion of a population chosen for a survey or experiment.
    • For example, say you want to survey what the most popular brand of soda is in America. Surveying the entire population would be too expensive and too time consuming. So you take a sample size which can be a few thousand Americans.
    • It’s important sample sizes are strategically chosen so it will be a reliable representation of all American’s and their soda preference.
  • The Standard Deviation is a measure that shows how spread out a set of data is. The symbol for Standard Deviation is σ (the Greek letter sigma) and is defined as the square root of the sample variance.
    • The formula for Standard Deviation:

Image via: GeographyFieldWork.com

  • The Sample Variance is a measure of the expected deviation from the mean. The symbol for Sample Variance is s2.
    • The formula for Sample Variance:

Description: http://www.statisticshowto.com/wp-content/uploads/2013/09/Variance_Formula.png

Image via: StatisticsHowTo.com

Head on over to MathisFun.com to read more about standard deviation and variance and learn how to solve for each.

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