# 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

The information is given as, 30% of customers shopping at SHOPNO will switch to DAILY SHOPPING every month on the other hand 40% of customers shopping at DAILY SHOPPING will switch to other every month. What is the probability that customers will switch from A to B for next two months?
Calculate correlation coefficient, where SP(xy) = 144; SS(x) = 739; SS(y) = 58. (2 Points)
The information are given from a randomly selected sample of age of COVID-19 patients who have already survived. These information are collected from 200 persons. The summarized information are as, n= 20; ∑x = 490; s^2 = 40. Calculate 95% confident interval of mean age.
Ashfat
The mode of the density of power of signal is 3.5. Find the probability that the density of a random signal will be more than 2.5.
Ashfat
The average time needed to repair a mobile phone set is 2 hours. If a customer is in queue for half an hour, what is the probability that his set will be repaired within 1.6 hours?
Ashfat
A quality control specialist took a random sample of n = 10 pieces of gum and measured their thickness and found the mean 9 and variance 0.04. Do you think that the mean thickness of the spearmint gum it produces is 8.4
3. The following are the number of mails received in different days by different organizations: Days (x) : 23, 35, 38, 50, 34, 60, 41, 32, 53, 67. Number of mails (y) : 18, 40, 52, 45, 32, 55, 50, 48, 26, 25. i) Fit a regression line of y on x and test the significance of regression. ii) Estimate y
The number of problem creating computers of two laboratories are as follows: Number of computers: 48, 6, 10, 12, 30, 11, 49, 17, 10, 14, 38, 25, 15, 19, 40, 12. Number of computers: 12, 10, 26, 11, 42, 11, 13, 12, 18, 5, 14, 38. Are the two laboratories similar in respect of problem creating compute
Is the severity of the drug problem in high school the same for boys and girls? 85 boys and 70 girls were questioned and 34 of the boys and 14 of the girls admitted to having tried some sort of drug. What can be concluded at the 0.05 level?
null rejected
Pratik
a quality control specialist took a random sample of n=10 pieces of gum and measured their thickness and found the mean 7.6 and standered deviation 0.10. Do you think that the mean thickness of the spearmint gum it produces is 7.5?
99. A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 10. Which of the following conclusions for the test would be correct? a
A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 10. Which of the following conclusions for the test would be correct?
Niaz
what is null Hypothesis
Niaz
what is null Hypothesis
Niaz
when median is greater than mode?
hello
Amaano
is this app useful
Worthy
little bit 😭
G-
oh
Worthy
when tail is positive
Jungjoon
define hypothesis
Worthy
I'm struggling to type it's on my laptop...statistics
Yoliswa
types of averages .mean median mode quarantiles MCQ question
what a consider data?
Out of 25 students, 15 are male. Is the overall proportion of male students 0.7 in AIUB? (4 Points)
15/25=0.6 or 60% standard calculation
Andrea
A quality control specialist took a random sample of n = 10 pieces of gum and measured their thickness and found the mean 7.6 and variance 0.01. Do you think that the mean thickness of the spearmint gum it produces is 7.5? (4 Points)
Omer
10 gums mean = 7.6 variance= 0.01 standard deviation= ? what us the data set?
Andrea
0.6
Rubina
A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. A pilot study was conducted to examine this hypothesis. Twelve older adults (over the age of 50) and twelve younger adults (between 20 and 40) were given a life satisfaction tes
how is it quantitative discrete data
আপেক্ষিক বিস্তার পরিমাপ কন টি