Statistics and Mechanics Chapter 2 - Measures of Location and Spread Flashcards
What is the modal value?
The value or class that occurs the most often.
What is the median?
The middle value when the data values are put in order.
How do you calculate x bar (the mean, which is symbolised by an x with a line over it)?
(Sum of x) divided by n. The sum of the data values divided by the number of data values.
What is the formula for the mean when the data is in a frequency table?
x bar = sum of xf / sum of f
How do you find the lower and upper quartiles?
For the LQ, divide n by 4. For the UQ, divide my 3/4 n. If the answer is a whole number, the quartile is halfway between that data point and the one above. If it is not a whole number, round UP and pick that data point.
What assumption are you making when you use interpolation on a frequency table?
You are assuming that the data values are evenly distributed within each class.
The formula for standard deviation.
The square root of the formula for variance. (Make sure to know the actual formula)
What is coding?
A way of simplifying statistical calculations. Each data value is coded to make a new set of data values which are easier to work with.
If data is coded using the formula y=(x-a)/b, what is the mean and standard deviation of the coded data?
Mean:
y bar = (x bar - a)/b
Standard deviation:
standard deviation of y = standard deviation of x/b
You would generally have to rearrange these equations to find x.
If the coding formula was x = (t - 20) / 2, what would you do differently to finding the mean when finding the standard deviation?
Multiply by 2 but don’t add 20. This is because if you add things the standard deviation will not change. (Imagine having a classroom full of people, and the standard deviation for the hight is 2cm. Then everyone stands on a chair, adding a foot to their height. The standard deviation is still 2cm because the heights have all increased by the same amount.)
