# 2.3 Descriptive statistics: histogram  (Page 2/4)

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• 68
• 68
• 69
• 69
• 69
• 69
• 69
• 69
• 69
• 69
• 69
• 69
• 69.5
• 69.5
• 69.5
• 69.5
• 69.5

• 70
• 70
• 70
• 70
• 70
• 70
• 70.5
• 70.5
• 70.5
• 71
• 71
• 71

• 72
• 72
• 72
• 72.5
• 72.5
• 73
• 73.5

• 74

The smallest data value is 60. Since the data with the most decimal places has one decimal (for instance, 61.5), we want our starting point to have two decimal places. Since the numbers 0.5, 0.05, 0.005, etc. are convenient numbers, use 0.05 and subtract it from 60, the smallest value, for the convenient starting point.

60 - 0.05 = 59.95 which is more precise than, say, 61.5 by one decimal place. The starting point is, then, 59.95.

The largest value is 74. 74+ 0.05 = 74.05 is the ending value.

Next, calculate the width of each bar or class interval. To calculate this width, subtract the starting point from the ending value and divide by the number of bars (you must choose the number of bars you desire). Suppose you choose 8 bars.

$\frac{74.05-59.95}{8}=1.76$
We will round up to 2 and make each bar or class interval 2 units wide. Rounding up to 2 is one way to prevent a value from falling on a boundary. Rounding to the next number is necessary even if it goes against the standard rules of rounding. For this example, using 1.76 as the width would also work.

The boundaries are:

• 59.95
• 59.95 + 2 = 61.95
• 61.95 + 2 = 63.95
• 63.95 + 2 = 65.95
• 65.95 + 2 = 67.95
• 67.95 + 2 = 69.95
• 69.95 + 2 = 71.95
• 71.95 + 2 = 73.95
• 73.95 + 2 = 75.95

The heights 60 through 61.5 inches are in the interval 59.95 - 61.95. The heights that are 63.5 are in the interval 61.95 - 63.95. The heights that are 64 through 64.5 are in the interval 63.95 - 65.95. The heights 66 through 67.5 are in the interval 65.95 - 67.95. The heights 68 through 69.5 are in the interval 67.95 - 69.95. The heights 70 through 71 are in the interval 69.95 - 71.95. The heights 72 through 73.5 are in the interval 71.95 - 73.95. The height 74 is in the interval 73.95 - 75.95.

The following histogram displays the heights on the x-axis and relative frequency on the y-axis.

The following data are the number of books bought by 50 part-time college students at ABC College. The number of books is discrete data since books are counted.

• 1
• 1
• 1
• 1
• 1
• 1
• 1
• 1
• 1
• 1
• 1

• 2
• 2
• 2
• 2
• 2
• 2
• 2
• 2
• 2
• 2

• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3
• 3

• 4
• 4
• 4
• 4
• 4
• 4

• 5
• 5
• 5
• 5
• 5

• 6
• 6

Because the data are integers, subtract 0.5 from 1, the smallest data value and add 0.5 to 6, the largest data value. Then the starting point is 0.5 and the ending value is 6.5.

Next, calculate the width of each bar or class interval. If the data are discrete and there are not too many different values, a width that places the data values in the middle of the bar or class interval is the most convenient. Since the data consist of the numbers 1, 2, 3, 4, 5, 6 and the starting point is 0.5, a width of one places the 1 in the middle of the interval from 0.5 to 1.5, the 2 in the middle of the interval from 1.5 to 2.5, the 3 in the middle of the interval from 2.5 to 3.5, the 4 in the middle of the interval from _______ to _______, the 5 in the middle of the interval from _______ to _______, and the _______ in the middle of the interval from _______ to _______ .

• 3.5 to 4.5
• 4.5 to 5.5
• 6
• 5.5 to 6.5

Calculate the number of bars as follows:

$\frac{6.5-0.5}{\mathrm{bars}}=1$

where 1 is the width of a bar. Therefore, $\mathrm{bars}=6$ .

The following histogram displays the number of books on the x-axis and the frequency on the y-axis.

## Using the ti-83, 83+, 84, 84+ calculator instructions

Go to the Appendix (14:Appendix) in the menu on the left. There are calculator instructions for entering data and for creating a customized histogram. Create the histogram for Example 2.
• Press Y=. Press CLEAR to clear out any equations.
• Press STAT 1:EDIT. If L1 has data in it, arrow up into the name L1, press CLEAR and arrow down. If necessary, do the same for L2.
• Into L1, enter 1, 2, 3, 4, 5, 6
• Into L2, enter 11, 10, 16, 6, 5, 2
• Press WINDOW. Make Xmin = .5, Xmax = 6.5, Xscl = (6.5 - .5)/6, Ymin = -1, Ymax = 20, Yscl = 1, Xres = 1
• Press 2nd Y=. Start by pressing 4:Plotsoff ENTER.
• Press 2nd Y=. Press 1:Plot1. Press ENTER. Arrow down to TYPE. Arrow to the 3rd picture (histogram). Press ENTER.
• Arrow down to Xlist: Enter L1 (2nd 1). Arrow down to Freq. Enter L2 (2nd 2).
• Press GRAPH
• Use the TRACE key and the arrow keys to examine the histogram.

## Optional collaborative exercise

Count the money (bills and change) in your pocket or purse. Your instructor will record the amounts. As a class, construct a histogram displaying the data. Discuss how many intervals you think is appropriate. You may want to experiment with the number of intervals. Discuss, also, the shape of the histogram.

Record the data, in dollars (for example, 1.25 dollars).

Construct a histogram.

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
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why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
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do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
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it is a goid question and i want to know the answer as well
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Abigail
for teaching engĺish at school how nano technology help us
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s.
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Tarell
what is the actual application of fullerenes nowadays?
Damian
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is Bucky paper clear?
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so some one know about replacing silicon atom with phosphorous in semiconductors device?
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for screen printed electrodes ?
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What is lattice structure?
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or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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