Question

(a) what is an empirical rule (b) why is empirical rule useful (c) Can the empirical rule be used on any population, why and why not?

A common way that statistics are misinterpreted or misleading, depending on how it's presented or when people assume relationships that exist at a group level held at the individual level. You are required to search for examples of misleading statistics, post a link to the article/ example, and discuss why and how it is misleading.

discuss your understanding of normal distribution; why is normal distribution important in statistics and in everyday life. Give examples to underscore your points.

Answer 1

(a) In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.

(b)The empirical rule, which states that nearly all data will fall within three standard deviations of the mean, can be useful in a few ways.

Explanation:

The empirical rule tells us about the distribution of data from a normally distributed population. It states that ~68% of the data fall within one standard deviation of the mean, ~95% of the data fall within two standard deviations, and ~99.7% of all data is within three standard deviations from the mean.

(c)The Empirical Rule is an approximation that applies only to data sets(populations) with a bell-shaped relative frequency histogram. It estimates the proportion of the measurements that lie within one, two, and three standard deviations of the mean but you can apply it to other distributions using Chebyshev's Theorem.

(d) Misleading statistics are simply the misusage – purposeful or not – of a numerical data. The results provide a misleading information to the receiver, who then believes something wrong if he or she does not notice the error or the does not have the full data picture.

Statistics Can Be Misleading in the following ways:

Examples:

1.When an experiment or a survey is led on a totally not significant sample size, not only will the results be unusable, but the way of presenting them – namely as percentages – will be totally misleading.

Asking a question to a sample size of 20 people, where 19 answer “yes” (=95% say for yes) versus asking the same question to 1,000 people and 950 answer “yes” (=95% as well): the validity of the percentage is clearly not the same. Providing solely the percentage of change without the total numbers or sample size will be totally misleading.

2. Colgate’s claim that 80% of dentists recommended the brand? You won’t be seeing that slogan again, at least not in the UK. Consumers were led to believe that 80% of dentists recommended Colgate while 20% recommended other brands. It turns out that when dentists were surveyed, they could choose several brands — not just one. So other brands could be just as popular as Colgate. This completely misleading statistic was banned by the Advertising Standards Authority.

(e) The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. For example, heights, blood pressure, measurement error, and IQ scores follow the normal distribution. It is also known as the Gaussian distribution and the bell curve.

The normal distribution is a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely.

Example of Normally Distributed Data: Heights

As you can see, the distribution of heights follows the typical pattern for all normal distributions. Most girls are close to the average (1.512 meters). Small differences between an individual’s height and the mean occur more frequently than substantial deviations from the mean. The standard deviation is 0.0741m, which indicates the typical distance that individual girls tend to fall from mean height.

The distribution is symmetric. The number of girls shorter than average equals the number of girls taller than average. In both tails of the distribution, extremely short girls occur as infrequently as extremely tall girls.

please rate my answer and comment for doubts.