Chapter 1: Exploring Data AP Statistics

Statistics Main Idea: The world would like to describe, discuss, etc. an entire “group,” i.e. all elements Problem: Too costly, time consuming, etc. to consider all elements Solution: The area of Statistics!

Definition Statistics—take a random selection from the entire group, a selection small enough to work with, and use the information in this representative group to describe, discuss, etc. the entire group. The art and science of data

Any set of data contains information about some group of individuals. The information is organized in variables. Individuals—objects described by a set of data. Variable—any characteristic of an individual. “Vary” from individual to individual Denoted by capital letters from the end of the alphabet, their values denoted by lower case letters example:X = agex = 22 Y = employment status y = “employed” or “not employed” Variables may be categorical, like y (qualitative) Variables may be numerical, like x (quantitative) There are variables that take numerical values that are not quantitative i.e. jersey number, social security number

Numerical values may be discrete or continuous. Discrete—set of possible values from a finite set or countable infinite set, i.e. integers. Continuous—possible values consist of entire interval on the number line; infinite possible values, i.e. decimals.

Data may be uni variate. This is data consisting of observations on a single variable. bi variate  2 variables multi variate  more than 2 variables

Q: What do we do with collected data? A: Two branches of statistics: (1) descriptive stats— provides a summary or description of collected data (2) inferential stats— generalizes from a sample to a population

Displaying Data: Categorical: bar graphs, pie charts Quantitative: univariate: (small data sets) dotplots, stemplots univariate: (large data sets) histograms bivariate: (large data sets) scatterplots A bar graph can be used for any set of categorical data, but a pie chart cannot. (page 10, Ex 1.3) page 11, Ex 1.4

Analyzing Data Once you have completed your display, you must analyze the distribution shown by the graph. The distribution is the set of all values of the variable being analyzed.

Describe the Overall Pattern: Remember your SOCS! S HAPE O UTLIERS C ENTER S PREAD

(1)Shape: (examples of descriptions) uniform unimodal (1 peak) bimodal (2 peaks) skew (“long tail” to right = skewed right) symmetry no apparent shape

Skewed LeftSkewed Right Symmetric

(2) Outliers: observations that fall outside the overall pattern ***If there are outliers, look for an explanation.*** (3)Center: Mean Median (4)Spread: Give the smallest and largest values, range

When values are too spread out for a reasonable dot plot, use a stemplot. (a)1. Title: Running Time of Hitchcock Films 2. Look at smallest/largest to construct stem 3. Order least to greatest 4. Key (b) 5. SOCS 6. Write mini paragraph

Hitchcock Films (a) Construct a stemplot of this distribution.

(b) Comment on the key features of this distribution (shape, center, spread, outliers) SOCS Symmetrical Possible outlier at 81 min Median at 116 min Range min The distribution of running times of Hitchcock films is fairly symmetrical, with a low outlier of 81 min. The center is about 116 min and the spread is from 81 to 136 min.

Histograms are the most common graphical display. Ex 1.6 p Divide into classes of equal width (least value of k for which 2 k > n, n = sample size) k = 62 6 = 64 > 43 2.Width = max – min = 69 – 42 = 4.5 # classes 6 use 5

3. ClassCount 40 - < < < < < < 703

4.Label, Scale, Title

More Practice with SOCS

symmetric

4 5 Slight left skew

4 5 uniform

4 bimodal

5 Left skew

Slight right skew