04.14.08

Assignment 1

Posted in Math, Uncategorized tagged , , , , , , at 9:48 pm by missreid

Shelly K Bernard
MTH332-01
Assignment 1

 
Definitions:

x: a data entry
n: total number of data entries
µ and \overline{x} : mean of x
σ : standard deviation of x

 

Equations:
Mean:

The term “mean” or “arithmetic mean” is preferred in mathematics and statistics to distinguish it from other averages such as the median and the mode. In mathematics and statistics, the (arithmetic) mean of a list of numbers is the sum of all the members of the list divided by the number of items in the list. Sample mean is typically denoted with a horizontal bar over the variable x; \overline{x} enunciated as “x bar”.

\mu = \overline{x} = \frac{1} {n}\sum_{i=1}^{n}x_i = \frac{x_1+x_2+...+x_n} {n}


Standard Deviation:

According to Wikipedia, the standard deviation of a probability distribution, random variable, or population/multiset of values is a measure of the spread of its values. It is usually denoted with the letter \sigma (lower-case sigma). It is defined as the square root of the variance, where the variance is the average of the squared differences between data points and the mean.

\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i-\mu)^2}

Z-score:

In statistics, a standard score is a quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing. The standard score indicates how many standard deviations an observation is above or below the mean. It allows comparison of observations from different normal distributions, which is done frequently in research. Standard scores are also called z-values, z-scores, normal scores, and standardized variables.

z-score = \frac{x-\mu}{\sigma}

 

Problem Assignment:
Using any data set, use R to complete the following tasks

Data entered into R:

This data is a representation of the percentage of 15 to 24 year olds who dropped out of high school from 1990 to 2001 which is defined in the report as an “even drop out rate.”

4.0 4.2 4.3 4.4 4.5 4.8 4.9 4.9 5.0 5.1 5.5 5.8

Histogram:

Click to see Histogram


Mean:

\mu = \overline{x} = \frac{1}{12}\sum_{i=1}^{12}x_i = \frac{x_1+x_2+...+x_{12}} {12}
mean(x) = 4.783333


Standard Deviation:

\sigma = \sqrt{\frac{1}{12}\sum_{i=1}^{12}(x_i-\mu)^2}
sd(x) = 0.5339958

Z-Score:

z-score = \frac{x_i-\mu}{\sigma}
= -1.46692789 -1.09239311 -0.90512572 -0.71785833 -0.53059094 0.03121123 0.21847862 0.21847862 0.40574601 0.59301340 1.34208296 1.9038851

Leave a Comment