# Ch 1.3 Frequency Distribution (GFDT)

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**Ch 1.3 Grouped Frequency Distribution Table (GFDT)**

Quantitative data can be summarized into a frequency table by classifying data into classes. Class can have a range of non-overlapping value with equal class width (difference between class lower class limits)

__Terms__ related to GFDT:

lower limits: lower bound of each class .

upper limits: upper bound of each class.

class midpoints: \( \dfrac{(lower + upper)}{2} \)

class width: difference between 2 consecutive lower limits.

class boundaries: values between 2 classes.

Ex.Given GFDT below: find lower limits, classwidth, class midpoints.

Because each class has one value, lower limits and upper limits are the same: 0, 1, 2, 3, 4, 5.

classwidth = 1

class midpoints: 0, 1, 2, 3, 4, 5

lower class limits: 60, 70, 80, 90

upper class limits: 69, 79, 89, 99

classwidth = 10

class midpoints: 64.5, 74.5, 84.5, 94.5

#### Relative and Cumulative frequency Distribution Table

Relative frequency and cumulative frequency can be evaluated for the classes. Because of rounding the relative frequency may not be sum to 1 but should be close to one.

__Rounding review__:

If the number **place** you are **rounding** is followed by 5, 6, 7, 8, or 9, **round** the **number** up.

If the **number place** you are **rounding** is followed by 0, 1, 2, 3, or 4, **round** the **number** down.

Ex1. Round to three decimal places:

a) 0.1278, b) 0.1283, c) 0.1239, d) 0.1298 e) 5/6

Ans: 0.1278 round to 0.128, 0.1283 round to 0.128, 0.1239 round to 0.124, 5/6 round to 0.833

Ex2. Round to 1 decimal place of a percent.

a) 0.1184 b) 45.677% c) 52/89

0.1184 is 11.84% round to 11.8%, 45.677% round to 45.7%, 52/89 round to 58.4%

Ex3. Round to the nearest whole number.

a) 12% of 781 b) 15.2% of 2344

a) 0.12 (781) =93.72 round to 94 b) 0.152(2344) =356.288 round to 356

Relative frequency for a class = \(\dfrac{\text{frequency for the class}}{\text {sum of all frequency}}\)

cumulative frequency =sum of the frequencies for that class and all previous classes

Ex1. Find relative and cumulative frequency for service time for a fast food restaurant given in the following GFDT.

total frequency = 50,

Relative frequencies: 11/50 = 0.22, 24/50 = 0.48, 10/50 = 0.2, 3/50 = 0.06, 2/50 = 0.02

class: less than 125, less than 175, less than 225, less than 275, less than 325

Cumulative frequencies: 11, 35, 45, 48, 50

##### Classes with overlapping class limits:

When frequency table has classes with overlapping limits at the end points, the common convention is

lower limit ≤ data < upper limit. or the classes are assigned so all data values fall between the limits.

Ex2. Find the percent of town with rainfall less than 9.01 in.

Total frequencies = 6 + 7+ 15 + 8 + 9 + 5 = 50

The first three classes has rainfall less than 9.01: (6 + 7 + 15)/50 = 0.56 = 56%

Frequency table where the class is time such as years.

Ex3. Find percent of crashes occurs after 2015.

Total frequencies = 30203 + 32744 + 35485 + 37809 + 37473 + 36560 = 210271

number of crashes after 2015 are at year 2016 to 2018 : 37806+37473+36560 = 111839

Percent = 111839/210271 = 53.2%

#### Graph a GFDT from data using online "socialscience calculator":

https://www.socscistatistics.com/descriptive/frequencydistribution/default.aspx

- -Find the minimum data value.
- - Enter data in a column in the input frame.
- - Click Generate.
- - select number of classes and the lowest class limits that should include the minimum data value and a nice value.
- - Click Edit frequency table for the new table.

Ex1. Construct a GFDT from the data below: use 7 classes and start with a “nice” good lowest limit.

Use socialscience calculator,

Input data to input frame. Click generate, then change class size to 7 and lowest class value to 20. Then click Edit frequency table.