Section 2.1-2.3 Statistics

ordered array

ordered list of data in order from largest to smallest or vice versa

distribution

way to describe the structure of a particular data set or population

frequency distribution

display of values that occurs in a data set and how often each value, or range of values, occurs

probability distribution

theoretical distribution used to predict the probabilities of particular data values occurring in a population

ungrouped frequency

frequency distribution when each category or class represents a single value

grouped frequency

frequency distribution where the classes are a range of values

Constructing a Frequency Distribution

1. Decide how many classes should be in distribution

2. Choose an appropriate class width (subtract the lowest number in the data set from the lowest number and divide the difference by the number of classes.) round the number up 4 a good start point to choose class width. choose a width so the classes present a clear representation of data and include all members of data set.

3. Find the class limit (lower class limit is the smallest number that can belong to a particular class and the upper class limit is the largest. You should shoes the first lower class limit so that the reasonable classes will be produced and it should have the same number of decimal places in the data. Add the class width to the lower limit of the first class to find the lower limit of second class

4. Determine the frequency of each class (make a tally mark for each data value in the appropriate class. found the marks to find the total frequency for each class)

Rounding rule

class limits should have the same number of decimal places as the largest number of decimal places in the data

characteristics of a frequency distribution

class boundary, class midpoint, relative frequency, cumulative frequency

Class Boundary

the value that lies halfway between the upper limit of one class and the lower limit of the next. after finding one class boundary add(or subtract) the class width to find the next class boundary. interval form (lower boundary, upper boundary)

class midpoint

the value in the middle of the class, and is given by

class midpoint = lower limit + upper limit / 2

relative frequency

the fraction or percentage of the data set that falls into a particular class given by f/n.

f: class frequency

n: the sample size given by n = ∑ f subscribe i

f subscript i is the frequency of the i ^th class.

cumulative frequency

sum of the frequencies of a given class and all previous classes. the cumulative frequency of the last class equals the sample size

categorical variable

places an individual into one of several groups or categories

-to display the distribution of this graph, use a pie chart or bar graph

quantitive variable

takes numerical values for which arithmetic operations such as adding and averaging make sense

time-series graph

line graph that is used to display a variable whose values change over time

pie chart

shows how large each category is in relation to the whole

-displays qualitative or categorical data

-uses relative frequencies from the frequency distribution to divide the pie into different wedges.

-Size or central angle measure of each wedge = relative frequency of each class * 360 and rounded to the nearest whole degree

frequency histogram

shortened to histogram, is a bar graph of frequency distribution of quantitative date

relative frequency histogram

heights of bars represent the relative frequencies of each class rather than just the frequencies

stem-and-leaf plot

graph of quantitative data that’s similar to a histogram in the way that it visually displays the distribution

-leaves are usually the last digit in each data value and the stems are the remaining digits

line graph

used when data is measurements over time. horizontal axis represents time. vertical axis represents the variable being measured. straight lines are used to connect points plotted at the value of each measurement above the time it was taken

cross-sectional graph

displays information collected at only one point in time

pictograph/pictogram

display information collected at only one point in time

Beware the Pictogram

• check to make sure all bars have the same width

• make the bars equally wide

• make sure the graph is scaled properly

• if you sketch or shrink the scale on the y-axis, the shape of the graph may change dramatically

• a line that rises gently on one scale might look very steep with a different scale

interpreting histograms

in any graph of data look for an overall pattern and for striking deviations from that pattern

an outlier is any graph of data is an individual observation that falls outside the overall pattern of the graph

to see the overall pattern of a histogram, ignore any outliers

shapes of graphs

1. uniform

2. symmetric

3. skewed to the right

4. skewed to the left

unifrom

frequency of each class is relatively the same

symmetrical

the data lie evenly on both sides of the distribution

skewed to the right

majority of the data fall on the left side of the distribution. the “tail” of the distribution is on the right

skewed to the left

the majority of the data fall on the right side of the distribution. the “tail” of the distribution is on the left