Statistics Chapter 2

Heights of adult males are known to have a normal distribution. A researcher claims to have randomly selected adult males and measured their heights with the resulting relative frequency distribution as shown here. Identify two major flaws with these results. Height (cm) Relative Frequency 130 to 144 23% 145 to 159 24% 160 to 174 21% 175 to 189 27% 190 to 204 28%

All of the relative frequencies appear to be roughly the same. If they are from a normal​ distribution, they should start​ low, reach a​ maximum, and then decrease. The sum of the relative frequencies is 123%, but it should be​ 100%, with a small possible​ round-off error

Refer to the table summarizing service times​ (seconds) of dinners at a fast food restaurant. How many individuals are included in the​ summary? Is it possible to identify the exact values of all of the original service​ times? Time (sec) Frequency 60 to 119 9 120 to 179 22 180 to 239 14 240 to 299 2 300 to 359 5

How many individuals are included in the summary? 9 + 22 + 14 + 2 + 5 = 52 Is it possible to identify the exact values of all of the original service​ times? No. The data values in each class could take on any value between the class​ limits, inclusive.

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Age (yr) when award was won Frequency 10 to 14 29 15 to 19 32 20 to 24 13 25 to 29 3 30 to 34 6 35 to 39 2 40 to 44 2

Identify the lower class limits. 10, 15, 20, 25, 30, 35, 40 Identify the upper class limits. 14, 19, 24, 29, 34, 39, 44 Identify the class width. 15 - 10 = 5 Class width = 5 Identify the class midpoints. 10 + 14 = 24 / 2 = 12 15 + 19 = 34 / 2 = 17 20 + 24 = 44 / 2 = 22 25 + 29 = 54 / 2 = 27 30 + 34 = 64 / 2 = 32 35 + 39 = 74 / 2 = 37 40 + 44 = 84 / 2 = 42 Identify the class boundaries. 9.5, 14.5, 19.5, 24.5, 29.5, 34.5, 39.5, 44.5 Identify the number of individuals included in the summary. 29 + 32 + 13+ 3 + 6 + 2 + 2 = 87

class width

The difference between the lower class limit of one class and the lower class limit of the next class.

Distribution

The nature or shape of the data

Class boundaries

The numbers used to separate classes, but without the gaps created by class limits For example: Age of Actresses Boundaries Frequency 20.5 21 - 30 30.5 28 31 - 40 40.5 30 41 - 50 50.5 12 51 - 60 60.5 2 61 - 70 70.5 2 71 - 80 80.5 2

Procedure for Constructing a Frequency Distribution

1. Decide on the number of classes you want. The number of classes should be between 5 and 20, and the number you select might be affected by convenience of using round numbers. 2. Calculate the Class Width: Class Width = (Max Value - Min Value) ---------------------------- Number of Classes Round the result to get a convenient number (usually up) you might need to change the number of classes but the priority should be to use values that are easy to understand.

Variation

A measure of the amount that data values vary among themselves.

The Center (of Data)

A representative or average value that indicates where the middle of that data set is located.

Frequency Table (or Frequency Distribution)

Lists data values (either individually or by groups or intervals), along with their corresponding frequencies (or counts).

Lower Class Limits

The smallest numbers that can belong to the different classes.

Time

changing characteristics of the data over time

Upper Class Limits

the largest numbers that can belong to the different classes

Class midpoints

Class midpoints are the values in the middle of the classes. Each class midpoint can be found by adding the lower class limit to the upper class limit and dividing the sum by 2. Remember to type integers or​ decimals, to not​ round, and to use ascending order.

Outliers

Sample values hat lie very far away from the majority of sample values