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National average checking account yield is 0.39 percent. But a few accounts offer 2 percent or more. Published Mon, May 11 2015 11:40 AM EDT Updated Thu, Jun 2 2016 12:33 PM EDT. Minnesota Birth Data 2017; Minnesota Birth Data 2017 State Rank. U.S. Percent of Births to Unmarried Mothers: 32.0: 45th: 39.8: Cesarean Delivery Rate: 27.4. If 5.0 g of NaOH are dissolved in water to give 250.0 g total mass of solution, what is the% concentration (w/w)? If a solution is 0.5% (w/v), how many mg/ml is that? How many grams of glucose must be added to 275 g of water in order to prepare percent by mass concentration of aqueous glucose solution 1.30%? In HoudahSpot 5, you can now make incremental adjustments to the default set up. For example, when you manage search locations, you will have the option to apply your changes to the default setup. HoudahSpot 5 adds support for modern macOS features like dark mode, Touch Bar, Finder extensions, and Quick Actions. HoudahSpot 5: User Guide 4.

Twenty students were asked how many hours they worked per day. Their responses, in hours, are as follows:
5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6, 5, 4, 4, 3, 5, 2, 5, 3.

The following table lists the different data values in ascending order and their frequencies.

Frequency Table of Student Work Hours
DATA VALUEFREQUENCY
23
35
43
56
62
71

In this research, 3 students studied for 2 hours. 5 students studies for 3 hours.

A frequency is the number of times a value of the data occurs. According to the table, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample.

A relative frequency is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample–in this case, 20. Relative frequencies can be written as fractions, percents, or decimals.

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Relative frequency = [latex]frac{text{frequency of the class}}{text{total}}[/latex]

Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row, as shown in the table below.

Cumulative relative frequency = sum of previous relative frequencies + current class frequency

Example 1

Frequency Table of Student Work Hours with Relative and Cumulative Relative Frequencies
DATA VALUEFREQUENCYRELATIVE

FREQUENCY

CUMULATIVE RELATIVE

FREQUENCY

23[latex]frac{3}{20}[/latex] or 0.150.15
35[latex]frac{5}{20}[/latex] or 0.250.15 + 0.25 = 0.40
43[latex]frac{3}{20}[/latex] or 0.150.40 + 0.15 = 0.55
56[latex]frac{6}{20}[/latex] or 0.300.55 + 0.30 = 0.85
62[latex]frac{2}{20}[/latex] or 0.100.85 + 0.10 = 0.95
71[latex]frac{1}{20}[/latex] or 0.050.95 + 0.05 = 1.00

The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.

Example 2

We sample the height of 100 soccer players. The result is shown below.

Height (inches)Frequency
59.95 – 61.955
61.95 – 63.953
63.95 – 65.9515
65.95 – 67.9540
67.95 – 69.9517
69.95 – 71.9512
71.95 – 73.957
73.95 – 75.951
Total = 100

Find:

a. the relative frequency for each class. Videopad 7 3700.

Show Answer
Height (Inches)FrequencyRelative FrequencyCumulative Relative Frequency
59.95 – 61.955[latex]frac{5}{100}[/latex] or 0.050.05
61.95 – 63.953[latex]frac{3}{100}[/latex] or 0.030.05 + 0.03 = 0.08
63.95 – 65.9515[latex]frac{15}{100}[/latex] or 0.150.08 + 0.15 = 0.23
65.95 – 67.9540[latex]frac{4}{100}[/latex] or 0.040.23 + 0.40 = 0.63
67.95 – 69.9517[latex]frac{17}{100}[/latex] or 0.170.63 + 0.17 = 0.80
69.95 – 71.9512[latex]frac{12}{100}[/latex] or 0.120.80 + 0.12 = 0.92
71.95 – 73.957[latex]frac{7}{100}[/latex] or 0.070.92 + 0.07 = 0.99
73.95 – 75.951[latex]frac{1}{100}[/latex] or 0.010.99 + 0.01 = 1.00
Total = 100Total = 1

b. the percentage for height that is less than 63.95 inches.

Show Answer

Houdahspot 5 0 11 Percent Auto Financing

c. the percentage for height that is between 69.95 inches and 73.95 inches.

Show Answer
[latex]frac{12}{100}[/latex] + [latex]frac{9}{100}[/latex] = 0.12 + 0.07 = 0.19

In this sample, there are five players whose heights fall within the interval 59.95–61.95 inches, three players whose heights fall within the interval 61.95–63.95 inches, 15 players whose heights fall within the interval 63.95–65.95 inches, 40 players whose heights fall within the interval 65.95–67.95 inches, 17 players whose heights fall within the interval 67.95–69.95 inches, 12 players whose heights fall within the interval 69.95–71.95, seven players whose heights fall within the interval 71.95–73.95, and one player whose heights fall within the interval 73.95–75.95. All heights fall between the endpoints of an interval and not at the endpoints.

Example 3

The table shows the amount, in inches, of annual rainfall in a sample of towns.

Rainfall (inches)Frequency
2.95 – 4.976
4.97 – 6.997
6.99 – 9.0115
9.01 – 11.038
11.03 – 13.059
13.05 – 15.075

Find

  1. the relative frequency and cumulative relative frequency for each class.
    Show Answer
    Total = sum of all frequencies = 6 + 7 + 15 + 8 + 9 + 5 = 50
    Rainfall (inches)FrequencyRelative frequencyCumulative relative frequency
    2.95 – 4.976[latex]frac{6}{50}[/latex] = 0.120.12
    4.97 – 6.997[latex]frac{7}{50}[/latex] = 0.140.12 + 0.14 = 0.26
    6.99 – 9.0115[latex]frac{15}{50}[/latex] = 0.300.26 + 0.30 = 0.56
    9.01 – 11.038[latex]frac{8}{50}[/latex] = 0.160.56 + 0.16 = 0.72
    11.03 – 13.059[latex]frac{9}{50}[/latex] = 0.180.72 + 0.18 = 0.90
    13.05 – 15.075[latex]frac{5}{50}[/latex] = 0.100.90 + 0.10 = 1.00
  2. the percentage of rainfall that is less than 9.01 inches.
    Show Answer
    The percentage of rainfall that is less than 9.01 inches = 0.12 + 0.14 + 0.30 = 0.56
  3. the percentage of heights that fall between 61.95 and 65.95 inches.
    Show Answer
    The percentage of heights that fall between 6.99 inches and 11.03 inches = [latex]frac{15}{50}[/latex] + [latex]frac{8}{50}[/latex] = 0.26

Try It

Houdahspot 5 0 11 Percent Percentage

The table contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.

YearTotal Number of Deaths
2000231
200121,357
200211,685
200333,819
2004228,802
200588,003
20066,605
2007712
200888,011
20091,790
2010320,120
201121,953
2012768
Total823,356
  1. What is the frequency of deaths measured from 2006 through 2009?
    Show Answer
  2. What percentage of deaths occurred after 2009?
    Show Answer
  3. What is the relative frequency of deaths that occurred in 2003 or earlier?
    Show Answer
  4. What is the percentage of deaths that occurred in 2004?
    Show Answer
  5. What kind of data are the numbers of deaths?
    Show Answer
  6. The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers?
    Show Answer

Example 4

Houdahspot 5

The table contains the total number of fatal motor vehicle traffic crashes in the United States for the period from 1994 to 2011.

Year
Total Number of CrashesYearTotal Number of Crashes
199436,254200438,444
199537,241200539,252
199637,494200638,648
199737,324200737,435
199837,107200834,172
199937,140200930,862
200037,526201030,296
200137,862201129,757
200238,491Total653,782
200338,477
  1. What is the frequency of deaths measured from 2000 through 2004?
    Show Answer
    37,526 + 37,862 + 38,491 + 38,477 + 38,444 = 190,800
  2. What percentage of deaths occurred after 2006?
    Show Answer
    [latex]frac{37,435 + 34,172 + 30,862 + 30,296 + 29,757}{653,782}[/latex] or 24.9%
  3. What is the relative frequency of deaths that occurred in 2000 or before?
    Show Answer
  4. What is the percentage of deaths that occurred in 2011?
    Show Answer
  5. What is the cumulative relative frequency for 2006? Explain what this number tells you about the data.
    Show Answer
    75.1% of all fatal traffic crashes for the period from 1994 to 2011 happened from 1994 to 2006.

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Houdahspot 5 0 11 Percent Fraction

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