Algebra/Statistics

Percentages

Percentages are another way of representing rational numbers. Rational numbers can be represented as decimals, fractions or percentages.

Percent, when you actually break the word apart, consists of two words: per and cent. Per is a small but extremly powerful word. It means "to divide". Cent is a Latin word for 100. Percent, then, means "divide by 100".

To convert from a fraction to a percentage, we simply multiply the fraction by 100. For example, $\frac{1}{4}=(\frac{1}{4}\times 100)\mathrm{\%}=25\mathrm{\%}$.

To convert from a decimal to a percentage, we first convert the decimal into a fraction, and then proceed with the approach outlined above. For example, $0.15=\frac{15}{100}=(\frac{15}{100}\times 100)\mathrm{\%}=15\mathrm{\%}$.

Measures of central tendency

Measures of central tendency are used to show and compare trends in a set of numerical data. These are:

Mean (average) - This measure shows the average value of data in a set and can be found by dividing the combined value of a data set by the number of individual data entered.
IE. 1,2,4,6,8,9 add to give a combined value of 30, which is then divided by the number of individual data (6), to give a mean of 5.

Mode - This measure shows the most frequently occurring value and can be found by counting the number of individual data that share the same value, the mode being the most commonly occurring value. In a situation where two or more different values occur the same number of times, and more than any other value, then that data set is said to have multiple modes. All of those values should be listed as the mode.
IE. 1,2,2,2,3,3,4,5,5,5,7 in this data set, the mode would be both 2 and 5, as both values occur the same number of times and more than any other value.

Median - This measure shows the value of the centre of a set of data when arranged in numerical order. The median value is that of whichever individual data has an equal number of data with higher values and lower values. In the case that there is an even number of data, the median is the mean of the two data values that are closest to the median.
IE. 2,2,3,4,4,5,6,7,8,9,12,13,16,22 in this data set, the median value lies between 6 and 7, and 6.5

Measures of spread

Range - The difference between the highest and lowest members of a set.

Quartile - The set of numbers in a quarter of the entire set.

Inter-Quartile Range - The difference between the highest and lowest members of a quartile

Upper Quartile - The quartile containing the top 25% of numbers in a set.

Lower Quartile - The quartile containing the bottom 25% of numbers in a set.