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The data can be put in order from lowest to highest: 20, 68, 80, 92.

The differences between the data have meaning. The score 92 is more than the score 68 by 24 points. Ratios can be calculated. The smallest score is 0. So 80 is four times 20. The score of 80 is four times better than the score of 20.

Frequency

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
.

[link] lists the different data values in ascending order and their frequencies.

Frequency table of student work hours
DATA VALUE FREQUENCY
2 3
3 5
4 3
5 6
6 2
7 1

A frequency is the number of times a value of the data occurs. According to [link] , 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.

Frequency table of student work hours with relative frequencies
DATA VALUE FREQUENCY RELATIVE FREQUENCY
2 3 3 20 or 0.15
3 5 5 20 or 0.25
4 3 3 20 or 0.15
5 6 6 20 or 0.30
6 2 2 20 or 0.10
7 1 1 20 or 0.05

The sum of the values in the relative frequency column of [link] is 20 20 , or 1.

Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies tothe relative frequency for the current row, as shown in [link] .

Frequency table of student work hours with relative and cumulative relative frequencies
DATA VALUE FREQUENCY RELATIVE
FREQUENCY
CUMULATIVE RELATIVE
FREQUENCY
2 3 3 20 or 0.15 0.15
3 5 5 20 or 0.25 0.15 + 0.25 = 0.40
4 3 3 20 or 0.15 0.40 + 0.15 = 0.55
5 6 6 20 or 0.30 0.55 + 0.30 = 0.85
6 2 2 20 or 0.10 0.85 + 0.10 = 0.95
7 1 1 20 or 0.05 0.95 + 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.

Note

Because of rounding, the relative frequency column may not always sum to one, and the last entry in the cumulative relative frequency column may not be one. However, they each should be close to one.

[link] represents the heights, in inches, of a sample of 100 male semiprofessional soccer players.

Frequency table of soccer player height
HEIGHTS
(INCHES)
FREQUENCY RELATIVE
FREQUENCY
CUMULATIVE
RELATIVE
FREQUENCY
59.95–61.95 5 5 100 = 0.05 0.05
61.95–63.95 3 3 100 = 0.03 0.05 + 0.03 = 0.08
63.95–65.95 15 15 100 = 0.15 0.08 + 0.15 = 0.23
65.95–67.95 40 40 100 = 0.40 0.23 + 0.40 = 0.63
67.95–69.95 17 17 100 = 0.17 0.63 + 0.17 = 0.80
69.95–71.95 12 12 100 = 0.12 0.80 + 0.12 = 0.92
71.95–73.95 7 7 100 = 0.07 0.92 + 0.07 = 0.99
73.95–75.95 1 1 100 = 0.01 0.99 + 0.01 = 1.00
Total = 100 Total = 1.00

The data in this table have been grouped into the following intervals:

  • 59.95 to 61.95 inches
  • 61.95 to 63.95 inches
  • 63.95 to 65.95 inches
  • 65.95 to 67.95 inches
  • 67.95 to 69.95 inches
  • 69.95 to 71.95 inches
  • 71.95 to 73.95 inches
  • 73.95 to 75.95 inches

Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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Kristine 2*2*2=8
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Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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AMJAD
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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Source:  OpenStax, Introductory statistics. OpenStax CNX. Aug 09, 2016 Download for free at http://legacy.cnx.org/content/col11776/1.26
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