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BASIC STATISTICS TERMS
 A statistic is a number that can be computed from the sample data without making use of any
parameters.
 A parameter is a number that describes the population usually its value is unknown.
 A probability of any outcome of a random phenomenon is the proportion of times the outcome
would occur in a very long series of repetitions.
 A sample space is the set of all possible outcomes of a random phenomenon.
 An event is any set of outcomes of interest.
 A probability of an event is the relative frequency of the outcomes over an infinite number of
trials.
 A random experiment is a mechanism that produces a definite outcome that cannot be
predicted with certainty. The sample space associated with a random experiment is the set of all
possible outcomes. An event is a subset of the sample space.
EXAMPLE #1: Construct a sample space for the random experiment that consists of tossing a single
coin.
EXAMPLE #2: Construct a sample space for a random experiment that consists of rolling a single dice.
Find the event of (1) an even number is rolled and (2) a number that is greater than two is rolled.
EXAMPLE #3: Construct a sample space that describes all three – child families according to the
genders of the children with respect to birth order. Find the events of (1) there are two boys in the
siblings, (2) there are two girls in the siblings and (3) there are three boys in the siblings.
𝐿𝑒𝑡 ℎ = ℎ𝑒𝑎𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑖𝑛
𝑡 = 𝑡𝑎𝑖𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑖𝑛
𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒 ∶ 𝑆 = ℎ, 𝑡
𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒 ∶ 𝑆 = 1, 2, 3, 4, 5, 6
𝐸𝑣𝑒𝑛𝑡 #1: 𝐸 = 2, 4, 6 → 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑠 𝑟𝑜𝑙𝑙𝑒𝑑
𝐸𝑣𝑒𝑛𝑡 #2: 𝐸 = 3, 4, 5, 6 → 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟 𝑡ℎ𝑎𝑡 𝑖𝑠 𝑔𝑟𝑒𝑡𝑎𝑒𝑟 𝑡ℎ𝑎𝑛 𝑡𝑤𝑜 𝑖𝑠 𝑟𝑜𝑙𝑙𝑒𝑑
𝐿𝑒𝑡 𝐵 = 𝑏𝑎𝑏𝑦 𝑏𝑜𝑦
𝐺 = 𝑏𝑎𝑏𝑦 𝑔𝑖𝑟𝑙
𝑁𝑂𝑇𝐸: 𝑌𝑜𝑢 𝑐𝑎𝑛 𝑢𝑠𝑒 𝑎 𝑡𝑟𝑒𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑦𝑜𝑢 𝑡𝑜 𝑘𝑛𝑜𝑤 𝑡ℎ𝑒 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑆 = 𝐵𝐵𝐵, 𝐵𝐵𝐺, 𝐵𝐺𝐵, 𝐵𝐺𝐺, 𝐺𝐵𝐵, 𝐺𝐵𝐺, 𝐺𝐺𝐵, 𝐺𝐺𝐺
𝐸1 = 𝐵𝐵𝐺, 𝐵𝐺𝐵, 𝐺𝐵𝐵 𝑡𝑤𝑜 𝑏𝑜𝑦𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑖𝑏𝑙𝑖𝑛𝑔𝑠
𝐸2 = 𝐵𝐺𝐺, 𝐺𝐵𝐺, 𝐺𝐺𝐵 𝑡𝑤𝑜 𝑔𝑖𝑟𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑖𝑏𝑙𝑖𝑛𝑔𝑠
𝐸3 = 𝐵𝐵𝐵 𝑡ℎ𝑟𝑒𝑒 𝑏𝑜𝑦𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑖𝑏𝑙𝑖𝑛𝑔𝑠
REVIEW EXERCISE

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Module01 basic statistics terms

  • 1. BASIC STATISTICS TERMS  A statistic is a number that can be computed from the sample data without making use of any parameters.  A parameter is a number that describes the population usually its value is unknown.  A probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions.  A sample space is the set of all possible outcomes of a random phenomenon.  An event is any set of outcomes of interest.  A probability of an event is the relative frequency of the outcomes over an infinite number of trials.  A random experiment is a mechanism that produces a definite outcome that cannot be predicted with certainty. The sample space associated with a random experiment is the set of all possible outcomes. An event is a subset of the sample space. EXAMPLE #1: Construct a sample space for the random experiment that consists of tossing a single coin. EXAMPLE #2: Construct a sample space for a random experiment that consists of rolling a single dice. Find the event of (1) an even number is rolled and (2) a number that is greater than two is rolled. EXAMPLE #3: Construct a sample space that describes all three – child families according to the genders of the children with respect to birth order. Find the events of (1) there are two boys in the siblings, (2) there are two girls in the siblings and (3) there are three boys in the siblings. 𝐿𝑒𝑡 ℎ = ℎ𝑒𝑎𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑖𝑛 𝑡 = 𝑡𝑎𝑖𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑖𝑛 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒 ∶ 𝑆 = ℎ, 𝑡 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒 ∶ 𝑆 = 1, 2, 3, 4, 5, 6 𝐸𝑣𝑒𝑛𝑡 #1: 𝐸 = 2, 4, 6 → 𝑎𝑛 𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑠 𝑟𝑜𝑙𝑙𝑒𝑑 𝐸𝑣𝑒𝑛𝑡 #2: 𝐸 = 3, 4, 5, 6 → 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟 𝑡ℎ𝑎𝑡 𝑖𝑠 𝑔𝑟𝑒𝑡𝑎𝑒𝑟 𝑡ℎ𝑎𝑛 𝑡𝑤𝑜 𝑖𝑠 𝑟𝑜𝑙𝑙𝑒𝑑 𝐿𝑒𝑡 𝐵 = 𝑏𝑎𝑏𝑦 𝑏𝑜𝑦 𝐺 = 𝑏𝑎𝑏𝑦 𝑔𝑖𝑟𝑙 𝑁𝑂𝑇𝐸: 𝑌𝑜𝑢 𝑐𝑎𝑛 𝑢𝑠𝑒 𝑎 𝑡𝑟𝑒𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑦𝑜𝑢 𝑡𝑜 𝑘𝑛𝑜𝑤 𝑡ℎ𝑒 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑆 = 𝐵𝐵𝐵, 𝐵𝐵𝐺, 𝐵𝐺𝐵, 𝐵𝐺𝐺, 𝐺𝐵𝐵, 𝐺𝐵𝐺, 𝐺𝐺𝐵, 𝐺𝐺𝐺 𝐸1 = 𝐵𝐵𝐺, 𝐵𝐺𝐵, 𝐺𝐵𝐵 𝑡𝑤𝑜 𝑏𝑜𝑦𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑖𝑏𝑙𝑖𝑛𝑔𝑠 𝐸2 = 𝐵𝐺𝐺, 𝐺𝐵𝐺, 𝐺𝐺𝐵 𝑡𝑤𝑜 𝑔𝑖𝑟𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑖𝑏𝑙𝑖𝑛𝑔𝑠 𝐸3 = 𝐵𝐵𝐵 𝑡ℎ𝑟𝑒𝑒 𝑏𝑜𝑦𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑖𝑏𝑙𝑖𝑛𝑔𝑠