Chapter 2: descriptive statistics

Example: 50-53 54-57 58-61 62-65 What are the midpoints?

1. (50+53)/2= 51.5 2.55.5 3. 59.5 4. 63.5

what is the class width? 1-4 5-8 9-12 13-16

4 (it goes up by 4)

Example: 50-53 54-57 58-61 What are the class boundaries?

49.5-53.5 53.5-57.5 57.5-61.5

frequency histogram -bar or line graph? -what data goes on the x axis? y axis?

A frequency histogram is a bar graph that represents the frequency distribution. A histogram has the following properties: 1) The horizontal scale is quantitative and measures the data values. 2) The vertical scale measures the frequencies of the classes. 3) Consecutive bars must touch. -bar, use midpoints for x axis, frequency for y

cumulative frequency graph or ogive -bar or line? -x axis ? y axis? -what do u need to add at the beginning of the graph?

A line graph that displays the cumulative frequency of each class at its upper class boundary. The upper boundaries are marked on the horizontal axis, and the cumulative frequencies are marked on the vertical axis -line -x: upper class boundaries (but start with the lowest boundary ) -y: cumulative frequency -dashes near the first midpoint

Constructing a Frequency Distribution 1. Decide the number of classes, should be between 5 and 20. *2) Find the class width. Divide the range (max - min) by the number of classes, and round up to the next convenient number. Ex-7 2.| becomes 3 3) Find class limits. Use the minimum data as the lower limit of the first class. Add class width to find the next lower limit. Find the upper limit, classes cannot overlap. 4) Make a tally mark of each entry. 5) Count the tally marks to find the total frequency of each class.

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Relative frequency histogram -bar or line? -what goes on x axis ? y axis?

a histogram that is using the relative frequency and it is the same as the shape of the Frequency Histogram. -bar -midpoints: x -relative frequency. *make sure the bars go into the next number*

Frequency Polygon -bar or line graph? -what goes on the x axis? y axis? -what do u need to add in the beginning of the graph and end?

a line graph that emphasizes the continuous change in frequencies -line, mid points, frequency -beginning: a break, dashes at the end. add the first and last number before the listed midpoint. for example: lowest midpoint is 9 and highest is 34. include 4 in the beginning near the break and 39 at the end near the dashes.

frequency distribution

a table showing classes or intervals of data entries with a count of the number of entries in each class. (basically just a table)

1-4 5-8 9-12 13-16 what are the lower class limits? upper?

lower- 1,5,9,13 upper: 4,8,12,16

How do u find class limits?

max-min divided by the number of classes

Frequency f

number of data entries in the class

Class boundaries

numbers that separate classes without forming gaps between them. The distance from the upper limit of the first class to the lower limit of the second class is 1. 54 - 53 = 1 divide by 2 is 0.5 Lower and upper boundaries of the first class are: 50 - 05 = 49 5 53 + 0.5 = 53.5

range

the difference between the maximum and minimum data entries

class width

the distance between lower (or upper) limits of consecutive classes

upper class limit

the greatest number that can belong to the class

relative frequency

the portion or percentage of data that falls in that class. -class frequency/sample size -use 3 digits. round the third digit. example: 0.1666 turns into 0.167

lower class limit

the smallest value within the class

cumulative frequency

the sum of the frequencies for that class and all previous classes. The cumulative frequency of the last class is equal to the sample size n.

Midpoint

the sum of the lower and upper limits of the class divided by two. The midpoint also called class mark.