10.2 Statistics Part 1

The study of statistics can be divided into two main areas The study of statistics can be divided into two main areas. _____________________________has to do with collecting, organizing, summarizing, and presenting data (information). _________________________- has to do with drawing inferences or conclusions about populations based on information from samples.

_____________________based on quantity, ability to be measured _____________________based on quantity, ability to be measured. (mathematical) The number of siblings in ten different families: 3, 1, 2, 1, 5, 4, 3, 3, 8, 2 Ex. ________________________based on qualities, descriptive, subjective, hard to measure. (englishy) The makes of five different automobiles:

When a data set includes many repeated items, it can be organized into a ___________________________, which lists the distinct values (x) along with their frequencies (f ). It is also helpful to show the _________________________of each distinct item. This is the fraction, or percentage, of the data set represented by each item.

Example: The ten students in a math class were polled as to the number of siblings in their individual families. Construct a frequency distribution and a relative frequency distribution for the responses below. 3, 2, 2, 1, 3, 4, 3, 3, 4, 2

The data from the previous example can be interpreted with special visual aids. ________________________- a series of rectangles, whose lengths represent the frequencies, are placed next to each other as shown below. *Similar to a bar graph but must have consecutive numbers and all bars touch

- plotting all points from frequency distribution and connected by lines.

Data sets containing large numbers of items are often arranged into groups, or classes. All data items are assigned to their appropriate classes, and then a grouped frequency distribution can be set up and a graph displayed. *Can be used with both quantitative and qualitative data.

Guidelines for the Classes of a Grouped Frequency Distribution 1. Make sure each data item will fit into one and only one, class. 2. Try to make all the classes the same width (not always possible or useful). 3. Make sure that the classes do not overlap. 4. Use from 5 to 12 classes.

Example: Twenty students, selected randomly were asked to estimate the number of hours that they had spent studying in the past week (in and out of class). The responses are recorded below. 15 58 37 42 20 27 36 57 29 42 51 28 46 29 58 55 43 40 56 36

________________________, which is similar to a histogram except that the rectangles (bars) usually are not touching each one another and sometimes are arranged horizontally rather than vertically.

________________________-which uses a circle to represent all the categories and divides the circle into sectors, or wedges (like pieces of pie), whose sizes show the relative magnitude of the categories. The angle around the entire circle measures 360°. For example, a category representing 20% of the whole should correspond to a sector whose central angle is 20% of 360° which is 72°.

Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers in the set tend to cluster, a kind of “middle” number or a measure of central tendency. Three such measures are discussed in this section.

Mean of a sample is denoted as: Mean of a population is denoted as: The ____________ (more properly called the _________________________) - of a set of data items is found by adding up all the items and then dividing the sum by the number of items. the “average.” Mean of a sample is denoted as: Mean of a population is denoted as:

Ten students in a math class were polled as to the number of siblings in their individual families and the results were: 3, 2, 2, 1, 3, 6, 3, 3, 4, 2. Find the mean number of siblings for the ten students.

Another measure of central tendency, which is not so sensitive to extreme values, is the _______________-. This measure divides a group of numbers into two parts, with half the numbers below the median and half above it.

To find the median of a group of items: Step 1 Rank the items. Step2 If the number of items is odd, the median is the middle item in the list. Step 3 If the number of items is even, the median is the mean of the two middle numbers.

Find the median for the distribution. Value 1 2 3 4 5 Frequency 6 8

The _______________ of a data set is the value that occurs the most often. Sometimes, a distribution is _______________ (literally, “two modes”). In a large distribution, this term is commonly applied even when the two modes do not have exactly the same frequency

Ten students in a math class were polled as to the number of siblings in their individual families and the results were: 3, 2, 2, 1, 3, 6, 3, 3, 4, 2. Find the mode for the number of siblings.

Find the mode for the distribution. Value 1 2 3 4 5 Frequency 6 8

Sometimes we want to look at a measure of _____________, or spread, of data. Two of the most common measures of dispersion are the range and the standard deviation.

For any set of data, the ___________ of the set is given by The two sets below have the same mean and median (7). Find the range of each set. Set A 1 2 7 12 13 Set B 5 6 8 9

One of the most useful measures of dispersion, the standard One of the most useful measures of dispersion, the standard deviation, is based on deviations from the mean of the data.