# 2.2 Descriptive statistics: histogram

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This module provides an overview of Descriptive Statistics: Histogram as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

For most of the work you do in this book, you will use a histogram to display the data. One advantage of a histogram is that it can readily display large data sets. A rule of thumb is to usea histogram when the data set consists of 100 values or more.

A histogram consists of contiguous boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents (for instance, distance from yourhome to school). The vertical axis is labeled either Frequency    or relative frequency . The graph will have the same shape with either label. The histogram (like the stemplot) can give you the shape of thedata, the center, and the spread of the data. (The next section tells you how to calculate the center and the spread.)

The relative frequency is equal to the frequency for an observed value of the data divided by the total number of data values in the sample. (In the chapter on Sampling and Data , we defined frequency as the number of times an answer occurs.) If:

• $f$ = frequency
• $n$ = total number of data values (or the sum of the individual frequencies), and
• $\mathrm{RF}$ = relative frequency,

then:

$\text{RF}=\frac{f}{n}$

For example, if 3 students in Mr. Ahab's English class of 40 students received from 90% to 100%, then,

$f=3$ , $n=\text{40}$ , and $\text{RF}=\frac{f}{n}=\frac{3}{\text{40}}=0\text{.}\text{075}$

Seven and a half percent of the students received 90% to 100%. Ninety percent to 100 % are quantitative measures.

To construct a histogram, first decide how many bars or intervals , also called classes, represent the data. Many histograms consist of from 5 to 15 bars or classes for clarity. Choose a starting point for the first interval to be less than the smallest data value. A convenient starting point is a lower value carried out to one more decimal place than the value with the most decimal places. For example, if the value with the most decimal places is 6.1 and this is the smallest value, a convenient starting point is 6.05 (6.1 - 0.05 = 6.05). We say that 6.05 hasmore precision. If the value with the most decimal places is 2.23 and the lowest value is 1.5, a convenient starting point is 1.495 (1.5 - 0.005 = 1.495). If the value with the most decimal places is 3.234 and the lowest value is 1.0, a convenient starting point is 0.9995 (1.0 - .0005 = 0.9995). If all the data happen to be integers and the smallest value is 2, then a convenient starting point is 1.5 (2 - 0.5 = 1.5). Also, when the starting point and other boundaries are carried to one additional decimal place, no data value will fall on a boundary.

The following data are the heights (in inches to the nearest half inch) of 100 male semiprofessional soccer players. The heights are continuous data since height is measured.

• 60
• 60.5
• 61
• 61
• 61.5

• 63.5
• 63.5
• 63.5

• 64
• 64
• 64
• 64
• 64
• 64
• 64
• 64.5
• 64.5
• 64.5
• 64.5
• 64.5
• 64.5
• 64.5
• 64.5

• 66
• 66
• 66
• 66
• 66
• 66
• 66
• 66
• 66
• 66
• 66.5
• 66.5
• 66.5
• 66.5
• 66.5
• 66.5
• 66.5
• 66.5
• 66.5
• 66.5
• 66.5
• 67
• 67
• 67
• 67
• 67
• 67
• 67
• 67
• 67
• 67
• 67
• 67
• 67.5
• 67.5
• 67.5
• 67.5
• 67.5
• 67.5
• 67.5

#### Questions & Answers

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Renato
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?
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research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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absolutely yes
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NANO
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s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
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Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Harper
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s.
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for screen printed electrodes ?
SUYASH
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Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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Cied
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how did you get the value of 2000N.What calculations are needed to arrive at it
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