# 2.3 Measures of the location of the data  (Page 5/15)

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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 percentile for 58.
2. Find the percentile for 25.
1. Counting from the bottom of the list, there are 18 data values less than 58. There is one value of 58.

x = 18 and y = 1. $\frac{x+0.5y}{n}$ (100) = $\frac{18+0.5\left(1\right)}{29}$ (100) = 63.80. 58 is the 64 th percentile.

2. Counting from the bottom of the list, there are three data values less than 25. There is one value of 25.

x = 3 and y = 1. $\frac{x+0.5y}{n}$ (100) = $\frac{3+0.5\left(1\right)}{29}$ (100) = 12.07. Twenty-five is the 12 th percentile.

## Try it

Listed are 30 ages for Academy Award winning best actors in order from smallest to largest.

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

Percentile for 47: Counting from the bottom of the list, there are 15 data values less than 47. There is one value of 47.

x = 15 and y = 1. $\frac{x+0.5y}{n}$ (100) = $\frac{15+0.5\left(1\right)}{29}$ (100) = 53.45. 47 is the 53 rd percentile.

Percentile for 31: Counting from the bottom of the list, there are eight data values less than 31. There are two values of 31.

x = 15 and y = 2. $\frac{x+0.5y}{n}$ (100) = $\frac{15+0.5\left(2\right)}{29}$ (100) = 31.03. 31 is the 31 st percentile.

## Interpreting percentiles, quartiles, and median

A percentile indicates the relative standing of a data value when data are sorted into numerical order from smallest to largest. Percentages of data values are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15 th percentile.

• Low percentiles always correspond to lower data values.
• High percentiles always correspond to higher data values.

A percentile may or may not correspond to a value judgment about whether it is "good" or "bad." The interpretation of whether a certain percentile is "good" or "bad" depends on the context of the situation to which the data applies. In some situations, a low percentile would be considered "good;" in other contexts a high percentile might be considered "good". In many situations, there is no value judgment that applies.

Understanding how to interpret percentiles properly is important not only when describing data, but also when calculating probabilities in later chapters of this text.

## Guideline

When writing the interpretation of a percentile in the context of the given data, the sentence should contain the following information.

• information about the context of the situation being considered
• the data value (value of the variable) that represents the percentile
• the percent of individuals or items with data values below the percentile
• the percent of individuals or items with data values above the percentile.

On a timed math test, the first quartile for time it took to finish the exam was 35 minutes. Interpret the first quartile in the context of this situation.

• Twenty-five percent of students finished the exam in 35 minutes or less.
• Seventy-five percent of students finished the exam in 35 minutes or more.
• A low percentile could be considered good, as finishing more quickly on a timed exam is desirable. (If you take too long, you might not be able to finish.)

#### Questions & Answers

In a survey of 100 stocks on NASDAQ, the average percent increase for the past year was 9% for NASDAQ stocks.
what is primary data and it's various types of collection of data?
If a random variable X takes only two values -2 and 1 such that 2 P[X=- 2]=P[X=1]=P, then find variance of x.
2.5
Anirban
how!
Alif
can u show the solution pls?
Punam
the mean of random variable following binomial distribution is 10. the numbers of trails are 30. What the approximate value of variance?
what is chis square
A chi-square (χ2) statistic is a test that measures how a model compares to actual observed data.
kalim
descriptive statistics basic
Sangeetha
Hi Friends
Sangeetha
tamil people yaaraavathu irukkingala
Sangeetha
what is the median of the following set of number:3,3,3,4,5,6,7,8,8,9?
3
Mbemah
5.6
Alekya
(5+6)/2=5.5555.......=5.6
Lyrical
(5+6)/2=5.5 that is the median
moniba
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nathan
hi friends am new here, hope am welcome
nathan
1.5
nathan
differences between Intervals and Ratio measurement scales
interval is the distinct from a starting point to the peak of a certain distance
Mbemah
the taking of a certain range accurately in a divisional way
Mbemah
i need the solution for exercise sums
descriptive statistics sums I need
Sangeetha
statistics discovered?
internet
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dev OS
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searching for motivation to learn stat
Nija
purpose of of statistics
mukesh
ya..
mukesh
tamil people yaraavathu inrukkingala
Sangeetha
Odisha ru kau bhai mane achha?
Hemanta
I want to learn my MSC by statistics who can help me ?
Abebe
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Abebe
good morning
Sangeetha
Dr good morning
mukhtar
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Yes
lukman
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Syed
The lower class boundary is found by subtracting 0.5 units from the lowerclass limit and the upper class boundary is found by adding 0.5 units to the upper class limit. The difference between the upper and lowerboundaries of any class.
Ekene
The lower class boundary is found by subtracting 0.5 units from the lowerclass limit and the upper class boundary is found by adding 0.5 units to the upper class limit. The difference between the upper and lowerboundaries of any class.
Ekene
complete definition plz
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advantage of primary data 1) specific 2) Accurate 3)ownership 4)up to date information 5) control Disadvantage of primary data 1) Expensive 2) time consuming 3) feasibility.
Xaib
the average increase for all NASDAQ stocks is the
formula of poisson probability distribution