# 2.3 Measures of the location of the data  (Page 7/15)

 Page 7 / 15

## References

Cauchon, Dennis, Paul Overberg. “Census data shows minorities now a majority of U.S. births.” USA Today, 2012. Available online at http://usatoday30.usatoday.com/news/nation/story/2012-05-17/minority-birthscensus/55029100/1 (accessed April 3, 2013).

Data from the United States Department of Commerce: United States Census Bureau. Available online at http://www.census.gov/ (accessed April 3, 2013).

“1990 Census.” United States Department of Commerce: United States Census Bureau. Available online at http://www.census.gov/main/www/cen1990.html (accessed April 3, 2013).

Data from San Jose Mercury News .

Data from Time Magazine ; survey by Yankelovich Partners, Inc.

## Chapter review

The values that divide a rank-ordered set of data into 100 equal parts are called percentiles. Percentiles are used to compare and interpret data. For example, an observation at the 50 th percentile would be greater than 50 percent of the other obeservations in the set. Quartiles divide data into quarters. The first quartile ( Q 1 ) is the 25 th percentile,the second quartile ( Q 2 or median) is 50 th percentile, and the third quartile ( Q 3 ) is the the 75 th percentile. The interquartile range, or IQR , is the range of the middle 50 percent of the data values. The IQR is found by subtracting Q 1 from Q 3 , and can help determine outliers by using the following two expressions.

• Q 3 + IQR (1.5)
• Q 1 IQR (1.5)

## Formula review

$i=\left(\frac{k}{100}\right)\left(n+1\right)$

where i = the ranking or position of a data value,

k = the kth percentile,

n = total number of data.

Expression for finding the percentile of a data value: (100)

where x = the number of values counting from the bottom of the data list up to but not including the data value for which you want to find the percentile,

y = the number of data values equal to the data value for which you want to find the percentile,

n = total number of data

Listed are 29 ages for Academy Award winning best actors in order from smallest to largest.

18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77

1. Find the 40 th percentile.
2. Find the 78 th percentile.
1. The 40 th percentile is 37 years.
2. The 78 th percentile is 70 years.

Listed are 32 ages for Academy Award winning best actors in order from smallest to largest.

18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77

1. Find the percentile of 37.
2. Find the percentile of 72.

Jesse was ranked 37 th in his graduating class of 180 students. At what percentile is Jesse’s ranking?

Jesse graduated 37 th out of a class of 180 students. There are 180 – 37 = 143 students ranked below Jesse. There is one rank of 37.

x = 143 and y = 1. $\frac{x+0.5y}{n}$ (100) = $\frac{143+0.5\left(1\right)}{180}$ (100) = 79.72. Jesse’s rank of 37 puts him at the 80 th percentile.

1. For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or a low percentile when running a race?
2. The 20 th percentile of run times in a particular race is 5.2 minutes. Write a sentence interpreting the 20 th percentile in the context of the situation.
3. A bicyclist in the 90 th percentile of a bicycle race completed the race in 1 hour and 12 minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the 90 th percentile in the context of the situation.
1. For runners in a race, a higher speed means a faster run. Is it more desirable to have a speed with a high or a low percentile when running a race?
2. The 40 th percentile of speeds in a particular race is 7.5 miles per hour. Write a sentence interpreting the 40 th percentile in the context of the situation.
1. For runners in a race it is more desirable to have a high percentile for speed. A high percentile means a higher speed which is faster.
2. 40% of runners ran at speeds of 7.5 miles per hour or less (slower). 60% of runners ran at speeds of 7.5 miles per hour or more (faster).

On an exam, would it be more desirable to earn a grade with a high or low percentile? Explain.

Mina is waiting in line at the Department of Motor Vehicles (DMV). Her wait time of 32 minutes is the 85 th percentile of wait times. Is that good or bad? Write a sentence interpreting the 85 th percentile in the context of this situation.

When waiting in line at the DMV, the 85 th percentile would be a long wait time compared to the other people waiting. 85% of people had shorter wait times than Mina. In this context, Mina would prefer a wait time corresponding to a lower percentile. 85% of people at the DMV waited 32 minutes or less. 15% of people at the DMV waited 32 minutes or longer.

In a survey collecting data about the salaries earned by recent college graduates, Li found that her salary was in the 78 th percentile. Should Li be pleased or upset by this result? Explain.

In a study collecting data about the repair costs of damage to automobiles in a certain type of crash tests, a certain model of car had $1,700 in damage and was in the 90 th percentile. Should the manufacturer and the consumer be pleased or upset by this result? Explain and write a sentence that interprets the 90 th percentile in the context of this problem. The manufacturer and the consumer would be upset. This is a large repair cost for the damages, compared to the other cars in the sample. INTERPRETATION: 90% of the crash tested cars had damage repair costs of$1700 or less; only 10% had damage repair costs of $1700 or more. The University of California has two criteria used to set admission standards for freshman to be admitted to a college in the UC system: 1. Students' GPAs and scores on standardized tests (SATs and ACTs) are entered into a formula that calculates an "admissions index" score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state. In this context, what percentile does the top 12% represent? 2. Students whose GPAs are at or above the 96 th percentile of all students at their high school are eligible (called eligible in the local context), even if they are not in the top 12% of all students in the state. What percentage of students from each high school are "eligible in the local context"? Suppose that you are buying a house. You and your realtor have determined that the most expensive house you can afford is the 34 th percentile. The 34 th percentile of housing prices is$240,000 in the town you want to move to. In this town, can you afford 34% of the houses or 66% of the houses?

You can afford 34% of houses. 66% of the houses are too expensive for your budget. INTERPRETATION: 34% of houses cost $240,000 or less. 66% of houses cost$240,000 or more.

Use [link] to calculate the following values:

First quartile = _______

Second quartile = median = 50 th percentile = _______

4

Third quartile = _______

Interquartile range ( IQR ) = _____ – _____ = _____

6 – 4 = 2

10 th percentile = _______

70 th percentile = _______

6

what is permutation
how to construct a histogram
I really appreciate that
I want to test linear regression data such as maintenance fees vs house size. Can I use R square, F test to test the relationship? Is the good condition of R square greater than 0.5
yes of course must have use f test and also use t test individually multple coefficients
rishi
Alright
umar
hi frnd I'm akeem by name, I wanna study economics and statistics wat ar d thing I must do to b a great economist
akeem
Is R square cannot analysis linear regression of X vs Y relationship?
Mok
To be an economist you have to be professional in maths
umar
hi frnds
Shehu
what is random sampling what is sample error
@Nistha Kashyap Random sampling is the selection of random items (or random numbers) from the group. A sample error occurs when the selected samples do not truely represent the whole group. The can happen when most or all of the selected samples are taken from only one section of the group;
Ron
Thus the sample is not truely random.
Ron
What is zero sum game?
A game in which there is no profit & no loss to any of the both player.
Milan
Differences between sample mean & population mean
***keydifferences.com/difference-between-sample-mean-and-population-mean.html
Lucien
Not difference in the formula except the notation, sample mean is denoted by x bar and population mean is denoted by mu symbol. There is formula as well as notation between difference variance and standard deviations
Akash
Likely the difference would be in the result, unless the sample is an exact representation of the population (which is unlikely.)
Ron
what is data
Nii
Nii Avin - Data is just a simple way to refer to the numbers in the population, or in the sample used in your calculations.
Ron
what are the types of data
Nii
Data is the very pale android from the Star Trek Enterprise
Andrew
Am Emmanuel from Nigeria
Emmanuel
Am Qudus from Nigeria
Rasak
am Handson from Cameroon
Handson
what is a mode?
Handson
Nii - data is whatever you are sampling. Such as the number of students in each classroom.
Ron
Handson Ndintek - the mode is the number appearing most frequently. Example: 7 9 11 7 4 6 3 7 2. 7 is the mode. In a group such as 7 9 1 4 6 3, there is no mode because no number appears more often than any other.
Ron
hi I want to know how to find class boundary
Baalisi
give me the two types of data
qualitative and quantitative
phoenix
primary and secondary data
Peace
qualitative and quantitative
Prince
Using Cauchy Schwartz inequality,or prove that b2-b1-1=0
what is the ongoing probability that President Trump will remain in the position he has chosen as his viability of his cabinet as he runs for reelection in the primaries of 2020 election year
Terry
what is statistic?
it's a science of collection, organization, analysis and summarizing data to get useful information to make several types of conclusions.which can be used in real life.
anshika
what is the statistical probability that president Trump will remain in the white house after the election of 2020?
Terry
i agree with anshika is right but let me add that such decisions are made in face of uncertainty
Maureen
yes
Stephen
classification of statistic
statistic can classified into many types eassy to understand future values effect
Narendra
what is mean?
Jhasaketan
average value
Narendra
İ want to understand what is t test or neyma. Pearson test ans difference
Yasin
to test the hypotesis ho follws h1 l1/lo
Narendra
Hope this helps. There are three main types of averages. *mean -> average -> (X1+X2+X3+...+Xn) / n *mode -> the element within a set which occurs most. {3,4,5,8,12,3,4,3,3,56} mode = 3 *median -  {3,3,4,5,8,12,56} median = 5 OR {3,4,5,8,12,56} median = 6.5
Jack
conceptual approach to limits
how are limits derived?
lameck
an entire section of calculus is devoted to that explanation.
Pitior
what is statistics?
statistics :- can be defined as the branches of mathematics that deals with the summarizing, analysing,organization and interpretation of data.
Usman
well said
Venkat
can we find Z value on calculator with out using Z table
no
Pitior
why
Maham
can another way is possible ?
Maham
Well you could make a table. And as the function you use the one used at the z table
Luca
The normal function is only one way, so you can only try using different numbers until you get the probability that you have. So that is easier if you have a table
Luca
me don't know nothing about z table and don't know how to see the z value on table can you tell me please how see the value on table
Maham
The z table is the table of the standard normal distribution
Luca
You can look it up on internet, its easier than writing down the normal distribution function (with an integral) and doing a table in the calculator
Luca
OK thanks luca
Maham
yes use pnorm in r
Venkat
pnorm(2.3,mean=0,sd=1)
Venkat
pnorm?
Maham
do u have r software
Venkat
no
Maham
its with tht u will get
Venkat
Venkat
z mathportal calculator
Venkat
calculator
Venkat
OK venkat thanks
Maham
welcome
Venkat
have calculator but don't know how find z value
Maham
ti83
Venkat
hey guys I'm from computer background so what are the concepts I supposed to prepare for interview in statistics
Alwin
descriptive stats
Venkat
inferential stats
Venkat
outlier treatment
Venkat
boxplot
Venkat
ok
Alwin
assumption of linear regression
Venkat
logistic regression
Venkat
k means clustering
Venkat
exact syllabus?
Alwin
type. analytics vidya interview questions statistics
Venkat
listen. data also
Venkat
like this forum
Jameel
My question is "is it only stats?"
Jameel
wer is the problem
Venkat
how find straight line equation in regression
u can find using excel
Venkat
or r studio
Venkat
for regression
Venkat
shall i help
Venkat
im an expert
Venkat
by giving a value to x,y
Ibrokhim
first provide data
Venkat
ill solve and guve
Venkat
ive
Venkat
Maham
maham you posted data
Venkat
Venkat
ok
Maham
x:1,2,3,4,5 y:2,5,6,8,9
Maham
regredsion equation is
Venkat
y=0.9+1.7x
Venkat
reg eq is y=0.9+1.7x
Venkat
slope = 1.7
Venkat
yintercept = 0.9
Venkat
Venkat
thanx venkat naveen😊
Maham
welcome
Venkat