Three Types of Frequency Distributions

ORGANIZING DATA

A Frequency Distribution is the organization of raw data in table form, using classes and frequencies.

Three types of Frequency Distributions: 1) Categorical Frequency Distribution 2) Grouped Frequency Distribution 3) Ungrouped Frequency Distribution

Categorical Frequency Distribution groups the data into specific categories such as nominal or ordinal level data.

Grouped Frequency Distributions take data with a large range of values and group them into classes of equal width. It consists of: - Class Limits - Class Boundaries - Tally - Frequency - Cumulative Frequency Class limits should have the same place value as the data. Class boundaries should have one additional decimal place and end in a 5.

There should be between 5 and 20 classes. The class width should be an odd number. (lower limit of one class subtracted from the lower limit of the next class) Class midpoint is found by adding the lower and upper limits and dividing by 2. The classes must be mutually exclusive. The classes must be continuous. The classes must be exhaustive. The classes must be equal in width.

Constructing a Grouped Frequency Distribution

1) Determine the number of classes Find the highest and lowest value, subtract to find the range. Find the width by dividing the range by the number of classes and rounding up. Select a starting point(usually the lowest number or any convenient number lower than the lowest number): add the width to get the lower limits Find the upper limits Find the boundaries 2) Tally the data 3) Find the numerical frequency from the tallies. 4) Find the cumulative frequencies. Construct a frequency distribution using 7 classes for the record high temperatures in each of the 50 states.

112 100 127 120 134 118 105 110 109 112 110 118 117 116 118 122 114 114 105 109 107 112 114 115 118 117 118 122 106 110 116 108 110 121 113 120 119 111 104 111 120 113 120 117 105 110 118 112 114 114 The data below represents the number of miles per gallon that 30 selected SUV’s obtained in city driving. Construct a frequency distribution.

12 17 12 14 16 18 16 18 12 16 15 15 16 12 15 16 16 12 14 15 12 15 15 19 13 16 18 16 14 17 HISTOGRAMS, FREQUENCY POLYGONS AND OGIVES

A histogram is a graph that displays the data by using contiguous vertical bats of various heights to represent the frequencies of the classes.

Class boundaries are used along the horizontal axis and the frequencies are listed along the vertical axis.

A frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes. The frequencies are represented by the heights of the points. The edges of the graph are closed down to the horizontal axis.

The Ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution. Class boundaries are used on the horizontal axis.

A relative frequency graph changes the numerical frequencies to ratios by dividing the frequency by the total number of frequencies.

EX. Construct a Histogram, Frequency Polygon and Ogive for the following information.

Class Boundaries Frequency 99.5 – 104.5 2 104.5 – 109.5 8 109.5 – 114.5 18 114.5 – 119.5 13 119.5 – 124.5 7 124.5 – 129.5 1 129.5 – 134.5 1 Construct a relative frequency Histogram, Frequency Polygon, and Ogive for the information.

Class Boundaries Frequency 99.5 – 104.5 2 104.5 – 109.5 8 109.5 – 114.5 18 114.5 – 119.5 13 119.5 – 124.5 7 124.5 – 129.5 1 129.5 – 134.5 1 OTHER TYPES OF GRAPHS

A PARETO Chart is used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest. The bars should be equal width.

A time series graph is a line graph that represents data that occur over a specific period of time.

A PIE Graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.

A STEM AND LEAF Plot is a data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups or classes.

Construct a Pareto Chart from the table showing the average amount of money spent by a family of four in 1996.

Groceries $480 Housing $650 Car $350 Clothes $250 Make a time series graph for the sales of Robert’s Toy Company in 2002 in ($000)

Jan Feb March April May June 17 18 20 28 15 21

July Aug Sep Oct Nov Dec 19 14 12 22 32 57 Make a Pie Chart for the Franklyn Factory Sales in 2002.

Gadgets 278 Gidgets 324 Widgets 478 Things 515 Whats 314 Make a Stem and Leaf Plot for the following numbers.

215 239 212 245 226 228 246 213 247 225 236 223 221 248 237 242 218 236 232 238