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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, so 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 eight bars.

74.05 59.95 8 1.76

Note

We will round up to two and make each bar or class interval two units wide. Rounding up to two is one way to prevent a value from falling on a boundary. Rounding to the next number is often necessary even if it goes against the standard rules of rounding. For this example, using 1.76 as the width would also work. A guideline that is followed by some for the width of a bar or class interval is to take the square root of the number of data values and then round to the nearest whole number, if necessary. For example, if there are 150 values of data, take the square root of 150 and round to 12 bars or intervals.

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.

Histogram consists of 8 bars with the y-axis in increments of 0.05 from 0-0.4 and the x-axis in intervals of 2 from 59.95-75.95.

Try it

The following data are the shoe sizes of 50 male students. The sizes are continuous data since shoe size is measured. Construct a histogram and calculate the width of each bar or class interval. Suppose you choose six bars.
9; 9; 9.5; 9.5; 10; 10; 10; 10; 10; 10; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5; 10.5
11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11; 11.5; 11.5; 11.5; 11.5; 11.5; 11.5; 11.5
12; 12; 12; 12; 12; 12; 12; 12.5; 12.5; 12.5; 12.5; 14

Smallest value: 9

Largest value: 14

Convenient starting value: 9 – 0.05 = 8.95

Convenient ending value: 14 + 0.05 = 14.05

14.05 8.95 6 = 0.85

The calculations suggests using 0.85 as the width of each bar or class interval. You can also use an interval with a width equal to one.

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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

Eleven students buy one book. Ten students buy two books. Sixteen students buy three books. Six students buy four books. Five students buy five books. Two students buy six books.

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
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Calculate the number of bars as follows:

6.5 0.5 number of bars 1

where 1 is the width of a bar. Therefore, bars = 6.

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

Histogram consists of 6 bars with the y-axis in increments of 2 from 0-16 and the x-axis in intervals of 1 from 0.5-6.5.
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Questions & Answers

which kind of work do statistics do
Adamu Reply
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Emefa Reply
?
a. l. bowley definition
Monster Reply
what are events in statistics
Animashaun Reply
Like a roll of a dice! Or a coin toss. Or a gender reveal party!
what is statistics
ADAM Reply
can anyone explain it better for me
ADAM
the science of statistics deal with the collection, analysis, interpretation and presentation of data
saquib
I am also studying statistics
saquib
Correlation regression, explain it to me in short.
guillio
correlation is used to find relationship between two and dependent ), regression used for predicting the future by analyzing past data
Arun
correlation is used to find relationship between two variables
Arun
dependent and independent eg. profit is dependent on sales
Arun
Statistics has been designed as the mathematical science of making decisions and drawing conclusions from data in situations of uncertainty. It includes the designings of experiments, collection, organization, summarization snd interpretation of numerical data.
Aliya
excellent Aliya..... good...Arun....
IRFAN
The degree or strength of relationship(interdependence) between the variables is called "correlation ". Examples: heights and weights of children, ages of husbands and ages of wives at the time of their marriages, marks of students in mathematics and in statistics.
Aliya
The dependence of one variable (dependent variable) one one or more independent variables ( independent variables) is called "regression ".
Aliya
simply regression and multiple regression are the types of regression.
Aliya
IRFAN HAIDER thanks
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nabil
I need help with a math problem
nabil
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umair
9. The scatterplot below relates wine consumption (in liters of alcohol from wine per person per year) and death rate from heart disease (in deaths per 100,000 people) for 19 developed countries.
nabil
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nabil
Rate from heart disease increases/decreases by ______deaths per ________people.
nabil
is a scientific study of collection analysis interpretation and also presenting it by researchers.
Murtala
frequency distribution
Wasim Reply
noun STATISTICS a mathematical function showing the number of instances in which a variable takes each of its possible values.
Robin
ok
ADAM
Common language-- taking a bunch of information and seeing if it is related or not to other info
Mandy
Does standard deviation have measuring unit?
Mohamed
yes, the measuring unit of the data you are looking at, for example centimetres for height.
Emma
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Mohamed
is that easy to plot a graph between three axis?
Mohamed
yes we can but we do not have that much effective tools. If the graph is normal or less complicated then it is plotted effectively otherwise it will give you nightmare.
umair
whats the difference between discrete and contineous data
umar
Discrete variables are variables that can assume finite number of values. Continuous variables are variables that can assume infinite number of values
Mike
i will give you an example: {0,4,84} it contains discrete or limited values like it can also contain boolean values{true,false} or {0,1} and continuous are like {1,2,3,4,5......} , {0,0.1,0.2,0.3,0.4...........}
umair
a no. of values which are countable are called discrete variables on the other hand, a no. of values which are not countable are called continuous variables
Aliya
Yup, I would like to support Mr.Umair's argument by saying that it can only apply if we have a 3-D graph,otherwise a plane graph will not apply at all
festus
Aliya and Mike thnks to both of you ❤❤
umar
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Noman
?
Sulaiman
what is covariance
Florence Reply
In probability theory and statistics, covariance is a measure of the joint variability of two random variables.[1] If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values, (i.e., the variables tend to show simila
Robin
Economics department, faculty of social sciences, NOUN. You are required to calculate: the covariance and State whether the covariance is positive or negative. (11½ marks) Observation E D 1 15 17.24 2 16 15.00 3 8 14.91 4 6 4.50 5 15 18.00 6 12 6.29 7 12 19.23 8 18 18.69 9 12 7.21 10 20 4
Florence
In probability theory and statistics, covariance is a measure of the joint variability of two random variables.
Robin
what is the purpose of statistics and why it is important that statistics to be a solo and one complete field?
Edu-info Reply
to organize,analyze and interpret information in order to make decision
Berema
what is noun?
Katama Reply
so simple. the name of any person,place or thing.
Edu-info
Using the Chi-square test, two coins were flipped a hundred times. What will be the chances of getting a head and getting a tale? Given observed values is 62 heads and 38 tails. Expected value is 50 heads, 50 tails. Is the difference due to chance or a significant error? a. Draw your hypothesis
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how do you get 2/50 ?
CL Reply
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korankye
an easier definition of inferential statistics
Kenedy Reply
Inferential statistics makes inferences and predictions about a population based on a sample of data taken from the population in question.
Rukhsana
Inferential statistics helps you to extract insights from a random sample data which then helps you to use specific predictive Modeling/machine learning technic to predict or forecast.
Manish
what is stemplot? can anyone explain?
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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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