DESCRIPTIVE STATISTICS CHAPTER TWO DESCRIPTIVE STATISTICS

Section 2.1 Frequency Distributions and Their Graphs

Frequency Distribution Def: a table that shows classes or intervals of the data entries with a count of the number of entries in each class, f. Frequency Distributions may also include: - Cumulative frequencies, cf. (running total) - Relative frequencies, rf. (% of total) - Class Midpoint (aka Class Mark) (sum of class limits, divided by 2)

Find (a) class width, (b) class midpoints, and (c) class boundaries Travel time to work (in minutes) Class Frequency, f 0 – 9 188 10 – 19 372 20 – 29 264 30 – 39 205 40 – 49 83 50 – 59 76 60 – 69 32

Construct a Frequency Distribution: Decide on the # of classes to include (between 5 and 20) Find the class width: range of the data divided by the # of classes, round UP if needed. Find the class limits: These are the lower and upper values for each class. Classes cannot overlap! Tally the data to find the frequency, f, for each class.

Construct a cumulative frequency distribution: Daily saturated fat intakes (in grams) for a sample of people: 38 32 34 39 40 54 17 29 33 57 25 36 24 42 16 31

Graphs of frequency distributions: Frequency Histogram: a bar graph that represents the distribution. 1. Horizontal scale = classes 2. Vertical scale = frequencies of classes 3. Consecutive bars touch - Use class BOUNDARIES on the horizontal scale. Frequency Polygon: a line graph that emphasizes the continuous change in frequencies. (Must start and end at 0 to close the shape)

Cumulative Frequency graph (OGIVE): a line graph that displays the cumulative frequency of each class at its upper boundary. 1. Horizontal scale: first lower boundary and all upper boundaries of the classes. 2. Vertical scale: frequencies 3. graph goes from 1st lower boundary (cf = 0) to last upper boundary (cf = n)

Relative Frequency Histogram: has the same shape as a frequency histogram, but uses the RELATIVE frequencies on the vertical axis.