Mean Deviations And Distributions.

Question 1

Week 2 covering: Mean deviation and distributions. (Quantitative skills 1).

Answer 1

Discussed:
-Population/samples continued

-Central limit theorem

-Descriptive statistics

-Measures of deviation from CT

z scores

Question 2

Week 2 covering: Mean deviation and distributions. Population and sample continued.

Answer 2

Last week you did a task on sampling methods
But what do we need to consider about sampling in general?

Population = the mean is fixed but unknown.*

Samples = the means vary with each sample, but are known.*

Question 3

Week 2 covering: Mean deviation and distributions. Normal distribution revisited.

Answer 3

If our samples contain more data points it is more likely that we will see a normal distribution (a bell curve) and more accurately estimate the population mean
Usually when we have over 30
data points is when we see
this happen!
But what else can help us estimate the population?

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution, while the parameter is its standard deviation.

Question 4

Week 2 covering: Mean deviation and distributions. Central limit theorem.

Answer 4

What is central limit theorem in simple terms?

The central limit theorem (CLT)states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population’s distribution

As the number of samples increases, the mean of these sample means will become closer to the population mean. The more samples we obtain, the better estimate we can get of the population mean.

When samples are above 30, the sampling distribution of the sample means will take the shape of a (or an approximate) normal distribution regardless of the shape of the population from which the sample was drawn.

Question 5

Week 2 covering: Mean deviation and distributions. Standard error theory.

Answer 5

There will always be a deviation from the sample means to the population mean
However, the mean of the sample means is a good estimation of the population mean
Therefore, sample means can tell us the degree to which the sample means deviate from the population mean
We can measure this by calculating the Standard Error
Provides an estimate of how well our sample mean represents the population mean - a lot of deviation will result in a larger SE.

Based on the normal distribution of sample means.
>
How well does our sample mean.
>
Represent the population mean.