Histograms

A Histogram is a graphical display of data using bars of different heights.

It is similar to a Bar Chart, but a

histogram groups numbers

into ranges

Histograms are used for data that is at least at the ordinal level (numbers) of measurement. The

classes for a histogram are ranges of values. Bars in a histogram cannot be rearranged. They must be

displayed in the order that the classes occur. Histograms are never drawn with spaces between the

bars.

The height of a bar corresponds to the relative frequency of the amount of data in the class. The

higher the bar, the higher the frequency (the more it occurs) of the data. The lower the bar, the lower

the frequency of data.

Histogram Example: Height of Orange Trees

You measure the height of every tree in the orchard in centimeters (cm)

The heights vary from 100 cm to 340 cm

You decide to put the results into groups of 50 cm:

The 100 to just below 150 cm range,

The 150 to just below 200 cm range,

etc...

a a tree that is 260 cm tall is added to the "250-300" range.

You can see (for example) that there are 30 trees from150 cm to just below 200 cm tall

Bar graphs measure the frequency of categorical data (For example suppose that I offered to

buy donuts for six people and three said they wanted chocolate covered, 2 said plain and one said

with icing sugar. An additional example could be those who like country, rock or jazz music), and the

classes for a bar graph are these categories. In a bar graph it is common practice to rearrange the

bars according to height.

Quadrilaterals

perpendicular planes

Net change-when you're done with EVERYTHING, how far did you move from the beginning.

Pattern/Rule-look for what repeats, changes, the rule must work for the entire sequence Prime Factorization-prime numbers multiplied together as factors to get a number Greatest Common Factor-GCF-largest factor the numbers share-factor x factor = product Least Common Multiple-LCM-smallest multiple the numbers share-multiples are the products you get when you multiply a number and another whole number Perimeter-units-distance around a closed figure Area-square units-number of square units needed to cover the inside of a closed figure Volume-cubic units-number of cubic units needed to fill a solid Surface Area-square inches-sum of all the areas of all the shapes that cover the surface of the object Constant Rate-Constant rate of change is a situation whereby the object is moving uniformly with respect to time. In simple terms, the two factors are increasing by the same proportions, though not necessarily the same figures. Varying Rate-changing

Transformations Create a graph, give it a title and use labels, predict what will happen next

Triangles are similar if they have the same shape, but can be different sizes.

(They are still similar even if one is rotated, or one is a mirror image of the other).

Rate of 1:3

Original triangle side length is 1, make new lengths 3xs bigger

circumference-distance around

the circle

Theoretical probability is what should happen, in theory. If we flip a coin, we should get tails

50% of the time, or 1 out of 2 times.

Theoretical Probability: # of favorable outcomes / # of possible outcomes

Experimental probability is a result of trials that test predictions. We flip a coin 50 times to see

how often it actually lands on tails. We must do a sufficient number of experiments.

Experimental Probability: # of favorable outcomes / # of trials

Acute Triangle-all angles smaller than right angles Obtuse Triangle-one angle larger than a right angle Right Triangle-one angle is a right angle Right angle-exactly ninety degrees Obtuse angle-larger than ninety degrees but smaller than a straight 180 degree angle Acute angle-smaller than a right angle Diagonal-connects two vertices that are not next to each other Equilateral Triangle-all sides same length Isosceles Triangle -at least two sides the same lengths Scalene Triangle -all sides different lengths double-two times as many congruent-same size, same shape interior angles- is an angle inside a shape ------------- exactly-no more, no less

frequency table- frequency is the number of times the data value occurs-put the results in a table is a frequency table create a scale model-make it similar to original (bigger or smaller) but keep same ratios for length, width and depth Dividing fractions No need to model? Then....

Area of a triangle

Modeling Multiplying Decimals

Exponents- 52means 5 times itself twice or 5 x5

N D

Order of Operations

Range-difference between the highest and lowest value Median-middle number when the data is in order Mode-number that shows up most often Mean- The mean is the average of the numbers: a calculated "central" value of a set of numbers. To calculate: Just add up all the numbers, then divide by how many numbers there are.

Equivalent Fractions-fractions that show the same amount