Week 9, Day 2

Today we explored data. It is often helpful to describe data by a single number that is most representative of an entire collection of numbers. Such a number is called a measure of central tendency. The most commonly used measures are as follows: Mean, or average, of n numbers is the sum of the numbers divided by n. The median of n numbers is the middle number when the numbers are written in order. If n is even, the median is the average of the two middle numbers. The mode of n numbers is the number that occurs most frequently. If two numbers tie for most frequent occurrence, the collection has two modes and is called bimodal. Quartiles are another concept we learned, and can be divided into two types: upper and lower. An upper quartile is the median of the numbers before m (the median of all numbers) and a lower quartile is the median of the numbers before m (the median of all numbers). Finally, we were taught measures of dispersion. The following are equations relating to variance and standard deviation: 

Example 1:

Given a set of numbers: 42. 62, 40, 29, 32, and 70, find the measures of central tendency. 

Then, using those values, determine the variance and standard of deviation.