Math Knowledge for Word Problems

4 times a number

4x

4 more than a number

x + 4

4 less than a number

x -4

4 times the difference of two numbers

4 (x-y)

Sum, And

x + y, addition

Difference

Subtraction, x-y

Product

Multiplication, xy

Number is, Equals to

= equal sign

IS/OF

18 is what percent of 42, of being denominator and is being the numerator.

Direct proportion

straight line function, if x moves so does y in proportion. It is linear.

Not directly proportional

Exponential functions, just cause x moves does not mean y moves at the same speed.

Mean

Average data set

Median

middle number of the data set, if two in the middle add together and divide by 2. average of the two.

Mode

most frequent number of the data set

Range

Distance between the lowest value number to the highest value number in a number set.

2 3 4 5 6 7 then range would be 7-2. L - H. L lowest, H Highest.

Shapes of distribution

Symmetry

Bimodial symmetry

You can draw a line in the middle fot he graph and it can split into two.

Bimodal mean is always equal to the median, likewise median is equal to the mean.

Unimodal symmetry

Mound shaped, like a pyramid. Mean, Median, and Mode are all equivalent to each other.

Uniform or rectangular

• Every category, value, or group (class) happens roughly the exact same number of times

• No mode, since there is no peaks

Skewness

Only one peak

Skewed data is lopsided. Instead of being nicely balanced like a bell curve, the data piles up on one side and stretches out (has a long "tail") on the other.

The "Toe" Trick (from the slide): Look at the little foot mnemonic in the diagram! Whichever direction the toes point tells you the type of skew:

• Left-Skewed: The long tail and the toes point to the left.

• Right-Skewed: The long tail and the toes point to the right.

=

Correlation/covariance

statistical measure that describes the relationship between two variables