Probability and Statistics Q-3

Probability

measure of how likely an event is to occur. It's a number between 0 and 1.

Statistics

describes only the sample

Random Variable

is a variable whose value is unknown or a function that assigns values to each of an experiment's outcomes. Are often designated by capital letters and can be classified as discrete, which are variable that have specific values, or continuous, which are variables that can have any values within a continuous range.

Discrete Random Variable

Its values are obtained through counting

Finite

Limited

Continuous Random Variable

Its values are obtained through measurement.

Probability distribution

of a discrete random variable summarizes its behavior, similar to a frequency distribution in a population.

Mean

The weighted average of all possible values the random variable assumes. It represents the long term average outcome over repeated trials.

Variance

Measures the spread or variability of the random variable's values around the mean.

Standard Deviation

The square root of the variance, showing how much the values deviate from the mean on average.

Variance of a random variable X

is denoted by a². It can likewise be written as Var(x). The ______________ is the expected value of the square of the difference between the assumed value of the random variable and the mean.

Standard deviation of a discrete random variable X

is denoted by 0. It is the square root of variance.

Variance and standard spread or variability

If the values of the variance and standard deviation are high, that means that the individual outcomes of the experiment are far relative to each other. In other words, the values differ greatly.

More scattered graph

has a higher variance and standard deviation because the data points are spread out

Tightly packed graph

has a lower variance and standard deviation since the value are closed together.

Normal distribution

is the most important distributions in statistics. Many researchers from different field use its idea in order to test their research hypotheses that will generate new knowledge and transform this knowledge into new applications that improve the quality of people’s lives.

Normal distribution or Normal curve

if a distribution contains a very large number of cases with equal measures of central tendency values, then the distribution is symmetrical and the skewness is 0.

Normal probability distribution

whenever the frequencies are converted to probabilities

Z table

which displays all the area of the region under the curve given a z value.

P(a<z<b)

this notation represents the idea stating the probability that the z value is between a and b.

P(z>a)

this notation represents the idea stating the probability that the z value is above a.

P(z<a)

this notation represents the idea stating the probability that the z value is below a where a and b are z

P(z=a) =0

this notation represents the idea stating the probability that the z value is equal to a is 0.

Percentile

is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. It is a measure of relative standing as it measures the relationship of a measurement of the rest of the data.

Population

group where members have something in common, that is, the total set of observations that can be made.

Sample

a smaller group or subset of the population in question.

Parameter

describes an entire population.

Simple Random Sampling

Where each member of the population has an equal chance of being. chosen as the sample. Example: •To choose the sample, arrange the elements. of the population in order, and then use a computer or a specific calculator to generate random numbers as required. The sample will be composed of those elements which correspond to the random numbers

Cluster Sampling

The population is first divided into separate groups called ______. Then, a simple random sampling of _____ from the available _______ in the population is selected. Example: •If the population is composed of all the senior citizens from Metro Manila, the clusters could be senior citizens from the different municipalities and cities in Manila Data is then gathered from selected clusters, like 5 cities. Metro Manila Data is then gathered from selected clusters, like 5 cities.

Systematic Random Sampling

This involves the random selection of one of the first k elements in an ordered population, and then the systematic selection of every kth element thereafter. The value of k is first calculated by dividing the population size by the sample size. Example: •Suppose there are 500 grade your sample. 5 students and you need to select 50 students as •Dividing the population size 500 by the sample size 50, we get 10. That means, every loth student will be included in the sample.

Stratified Random Sampling

This involves selecting a simple random sample from each of a given number of sub populations. Each subpopulation is called a stratum (plural; strata). Example: •If a study is taking senior citizens into consideration, the population may need to be subdivided into subgroups like 60-69 years old, 70-79 years old, etc. The sample will be chosen from each subgroup.

Multi stage Sampling

Two or more probability techniques are combined. It can be described as sampling within the sample. Example: •If the population is composed of all the senior citizens from Metro Manila, we can use clustered sampling where the clusters are the municipalities and cities in Metro Manila. •Then from the selected clusters, we can use stratified sampling and divided into different age groups.

POINT ESTIMATION

is the use of a suitable statistic and computes its value from a given sample data, that is use to estimate a parameter. The statistic use is called the _________, and the value of the statistic is called the point estimate.

Interval Estimation

is the use of sample data to calculate a range of possible values for an unknown population parameter. Unlike the point estimation that uses a single value, uses interval value.

Confidence interval

The ______ 11320 ≤ μ≤ 22580.

Confidence limits

The lower limit of the interval, 11320, and the upper limit, 22580, are called the ______.

Confidence level

The 95% level of confidence is called the confidence level. It can be noted that 95% _______ indicates that we might commit 5% error in estimating the mean.

Alpha (a)

The 5% level of error committed in estimating the mean is known as ________.