# 1.3 Frequency, frequency tables, and levels of measurement  (Page 4/14)

 Page 4 / 14

## Try it

From [link] , find the number of towns that have rainfall between 2.95 and 9.01 inches.

## Try it solutions

6 + 7 + 15 = 28 towns

## Collaborative exercise

In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has. Create a frequency table. Add to it a relative frequency column and a cumulative relative frequency column. Answer the following questions:

1. What percentage of the students in your class have no siblings?
2. What percentage of the students have from one to three siblings?
3. What percentage of the students have fewer than three siblings?

Nineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows:

• 2
• 5
• 7
• 3
• 2
• 10
• 18
• 15
• 20
• 7
• 10
• 18
• 5
• 12
• 13
• 12
• 4
• 5
• 10

Frequency of commuting distances
DATA FREQUENCY RELATIVE
FREQUENCY
CUMULATIVE
RELATIVE
FREQUENCY
3 3 $\frac{3}{19}$ 0.1579
4 1 $\frac{1}{19}$ 0.2105
5 3 $\frac{3}{19}$ 0.1579
7 2 $\frac{2}{19}$ 0.2632
10 3 $\frac{4}{19}$ 0.4737
12 2 $\frac{2}{19}$ 0.7895
13 1 $\frac{1}{19}$ 0.8421
15 1 $\frac{1}{19}$ 0.8948
18 1 $\frac{1}{19}$ 0.9474
20 1 $\frac{1}{19}$ 1.0000
1. Is the table correct? If it is not correct, what is wrong?
2. True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections.
3. What fraction of the people surveyed commute five or seven miles?
4. What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)?
1. No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct.
2. False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read: 0.1052, 0.1579, 0.2105, 0.3684, 0.4737, 0.6316, 0.7368, 0.7895, 0.8421, 0.9474, 1.0000.
3. $\frac{5}{19}$
4. $\frac{7}{19}$ , $\frac{12}{19}$ , $\frac{7}{19}$

## Try it

[link] represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year?

## Try it solutions

$\frac{9}{50}$

[link] contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.

Year Total Number of Deaths
2000 231
2001 21,357
2002 11,685
2003 33,819
2004 228,802
2005 88,003
2006 6,605
2007 712
2008 88,011
2009 1,790
2010 320,120
2011 21,953
2012 768
Total 823,356

1. What is the frequency of deaths measured from 2006 through 2009?
2. What percentage of deaths occurred after 2009?
3. What is the relative frequency of deaths that occurred in 2003 or earlier?
4. What is the percentage of deaths that occurred in 2004?
5. What kind of data are the numbers of deaths?
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?
1. 97,118 (11.8%)
2. 41.6%
3. 67,092/823,356 or 0.081 or 8.1 %
4. 27.8%
5. Quantitative discrete
6. Quantitative continuous

## Try it

[link] 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 Crashes Year Total Number of Crashes
1994 36,254 2004 38,444
1995 37,241 2005 39,252
1996 37,494 2006 38,648
1997 37,324 2007 37,435
1998 37,107 2008 34,172
1999 37,140 2009 30,862
2000 37,526 2010 30,296
2001 37,862 2011 29,757
2002 38,491 Total 653,782
2003 38,477

1. What is the frequency of deaths measured from 2000 through 2004?
2. What percentage of deaths occurred after 2006?
3. What is the relative frequency of deaths that occurred in 2000 or before?
4. What is the percentage of deaths that occurred in 2011?
5. What is the cumulative relative frequency for 2006? Explain what this number tells you about the data.

## Try it solutions

1. 190,800 (29.2%)
2. 24.9%
3. 260,086/653,782 or 39.8%
4. 4.6%
5. 75.1% of all fatal traffic crashes for the period from 1994 to 2011 happened from 1994 to 2006.

## References

“Table 5: Direct hits by mainland United States Hurricanes (1851-2004),” National Hurricane Center, http://www.nhc.noaa.gov/gifs/table5.gif (accessed May 1, 2013).

“Levels of Measurement,” http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Levels.htm (accessed May 1, 2013).

David Lane. “Levels of Measurement,” Connexions, http://cnx.org/content/m10809/latest/ (accessed May 1, 2013).

## Chapter review

Some calculations generate numbers that are artificially precise. It is not necessary to report a value to eight decimal places when the measures that generated that value were only accurate to the nearest tenth. Round off your final answer to one more decimal place than was present in the original data. This means that if you have data measured to the nearest tenth of a unit, report the final statistic to the nearest hundredth.

• Nominal scale level: data that cannot be ordered nor can it be used in calculations
• Ordinal scale level: data that can be ordered; the differences cannot be measured
• Interval scale level: data with a definite ordering but no starting point; the differences can be measured, but there is no such thing as a ratio.
• Ratio scale level: data with a starting point that can be ordered; the differences have meaning and ratios can be calculated.

When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these.

What type of measure scale is being used? Nominal, ordinal, interval or ratio.

1. High school soccer players classified by their athletic ability: Superior, Average, Above average
2. Baking temperatures for various main dishes: 350, 400, 325, 250, 300
3. The colors of crayons in a 24-crayon box
4. Social security numbers
5. Incomes measured in dollars
6. A satisfaction survey of a social website by number: 1 = very satisfied, 2 = somewhat satisfied, 3 = not satisfied
7. Political outlook: extreme left, left-of-center, right-of-center, extreme right
8. Time of day on an analog watch
9. The distance in miles to the closest grocery store
10. The dates 1066, 1492, 1644, 1947, and 1944
11. The heights of 21–65 year-old women
12. Common letter grades: A, B, C, D, and F
1. ordinal
2. interval
3. nominal
4. nominal
5. ratio
6. ordinal
7. nominal
8. interval
9. ratio
10. interval
11. ratio
12. ordinal

Uttam
How can I calculate the Class Mark, Relative frequency and the cumulative frequency on a frequency table?
what is the important in business planning and economics
explain the limitation and scope of statistics
mahelt
statistics is limited to use where data can be measured quantitatively. statistics scope is wider such as in economic planning, medical science etc.
Gurpreet
can you send me mcq type questions
Yas
Umar
which books are best to learn applied statistics for data science/ML
Gurpreet
A population consists of five numbers 2,3,6,8,11.consists all possible samples of size two which can be drawn with replacement from this population. calculate the S.E of sample means
A particular train reaches the destination in time in 75 per cent of the times.A person travels 5 times in that train.Find probability that he will reach the destination in time, for all the 5 times.
0.237
Amresh
umesh
p(x=5)= 5C0 p^5 q^0 solve this
Amresh
umesh
ok
umesh
5C0=1 p^5= (3/4)^5 q^0=(1/4)^0
Amresh
Hint(0.75 in time and 0.25 not in time)
kamugi
what is standard deviation?
It is the measure of the variation of certain values from the Mean (Center) of a frequency distribution of sample values for a particular Variable.
Dominic
what is the number of x
10
Elicia
Javed Arif
Jawed
how will you know if a group of data set is a sample or population
population is the whole set and the sample is the subset of population.
umair
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
Bhavika
hello everyone if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future? thanks
Alexander
Pls I hv a problem on t test is there anyone who can help?
Peggy
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
hi
Bhavika
hii Bhavika
Dar
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
Hoshyar
three coins are tossed. find the probability of no head
three coins are tossed consecutively or what ?
umair
umair
or .125 is the probability of getting no head when 3 coins are tossed
umair
🤣🤣🤣
Simone
what is two tailed test
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
umair
in this test you are worried on both the ends
umair
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
umair
In order to apply weddles rule for numerical integration what is minimum number of ordinates
excuse me?
Gabriel
why?
didn't understand the question though.
Gabriel
which question? ?
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
John
Someone should help me please, how can I calculate the Class Mark, Relative frequency and the cumulative frequency on a frequency table?
IJOGI
geometric mean of two numbers 4 and 16 is:
10
umair
really
iphone
quartile deviation of 8 8 8 is:
iphone
sorry 8 is the geometric mean of 4,16
umair
quartile deviation of 8 8 8 is
iphone
can you please expalin the whole question ?
umair
mcq
iphone
h
iphone
can you please post the picture of that ?
umair
how
iphone
hello
John
10 now
John
how to find out the value
can you be more specific ?
umair
yes
KrishnaReddy
what is the difference between inferential and descriptive statistics
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
umair
if you need more help i am up for the help.
umair
Thanks a lot
Anjali
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
fred
my pleasure😊. Helping others offers me satisfaction 😊
umair
inferential statistics the results of the statistical analysis of the sample data of the population are used for generalization or decision making about the population why descriptive statistics, the analyzed data are presented without generalization or decision making about the population.
IJOGI