STATISTICS AND PROBABILITY 4TH QUARTER

• Any measurable characteristic of a sample 


  Statistic
• Any measurable characteristic of a population

  Parameter
• Subset of the population


  Sample
• Entire Group

  Population
• The average weight of all males in the Philippines

  Parameter
• The average appliance sale price for 100 appliance sales that were randomly selected from all sales this year is ₱12,000

  Statistic
• The average test of 20 students in a class of 500

  Statistic
• The average height of 100 cats in the state of California

  Statistic
• The total number of cars sold in all branches of a car manufacturing company in 2019 is 5 million pesos

  Parameter
• x̄(Sample)

  Mean
• s (sample)

  Standard Deviation
• S² (Sample)


  Variance
• n (sample)


  Size
• μ (population)

  Mean
• σ (population)

  Standard Deviation
• σ2 (population)

  Variance
• N (Population)

  Size
• Is used to calculate an appropriate sample size from a population

  Slovin's Formula
• n= N/1+Ne²

  Slovin's Formula
• e

  Margin of Error
• Probability Sampling

  Simple Random Sampling

  Systematic Random Sampling

  Stratified Random Sampling

  Cluster Sampling
• Non- probability Sampling

  Convenience Sampling

  Qouta Sampling
• Probability sampling is a sampling technique, in which the subject of the population get an equal opportunity to be selected as a representative sample
• Simple Random Sampling

  Sampling is done by drawing lots or through the use of random numbers.

  The best example of this is a fish bowl method
• Example: A class list compromising of 50 names is cut into strips, rolled up, and put in a bowl. Ten strips (names) are then drawn from the bowl. The ten names that were picked are collectively called the simple random sample
• Systematic Random Sampling is done by selecting every ith element in the population with the starting point determined at random
• i = N/n

  Systematic Random Sampling
• Stratified Random Sampling is done by first dividing the population into a number of non- overlapping sub-populations or strata and then taking samples from each stratum
• Stratified Random Sampling

  Equal Allocation

  Proportional Allocation
• Equal Allocation

  ni= n/k

  n - intended sample size

  k- no. of Strata or sub-populations
• Proportional Allocation

  ni= (Ni/N) n

  Ni- Sub-population or stratum

  n- Intended Sample Size

  N - Population Size
• Cluster Sampling is done by dividing the population into (geographical) groups called clusters
• Non-probability sampling are chosen in such a way that some members of the population may not have any chance of being included in the sample
• Convenience Sampling

  Selecting those members of the population that are readily available in order to obtain quick results
• Quota Sampling

  Choosing members for the sample with no other criteria or objective but to obtain a certain target number whether or not based on the proportion of each stratum with the population
• Sampling Distribution of Sample Means is a frequency distribution using the means computed from all possible random samples of a specific size taken from a population.
• N !__ n!(N-n)! N = population size n = sample size x = sample mean μ = population mean P(x) = corresponding probability
• Steps in Constructing the Sampling Distribution of Sample Means

  1. Determine the number of sets of all possible random sample that can be drawn from the given population by using the formula, ɴCn, where N is the population size and n is the sample size.
  2. List all the possible samples and compute the mean of each sample.
  3. Construct the sampling distribution.
  4. Construct a histogram
• The mean of all values in the population - Population Mean
• The mean of sample Values collected - sample Mean