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Chapter 1: Q. 97 (page 72)

Phosphate levels The level of various substances in the blood influences our health. Here are measurements of the level of phosphate in the blood of a patient, in milligrams of phosphate per deciliter of blood, made on 6 consecutive visits to a clinic: 5.6, 5.2, 4.6, 4.9, 5.7, 6.4. A graph of only 6 observations gives little information, so we proceed to compute the mean and standard deviation. (a) Find the standard deviation from its definition. That is, find the deviations of each observation from the mean, square the deviations, then obtain the variance and the standard deviation. (b) Interpret the value of sx you obtained in (a)

Short Answer

Expert verified

a. x¯=5.4mg/dI and sx=0.6419mg/dI

b. The phosphate level varies at 0.6418 mg/dI

Step by step solution

01

Finding the value of the standard deviation  

a. the mean value of all question data is 5.6+5.2+4.6+4.95.7+6.46=5.4mg/dI

Assume xiis the data value then deviation is Xi-X. so the square deviation is

Now, the variance is the sum of the total values divided by (n-1).

sx2=0.04+0.04+0.06+0.25+0.09+16-1=0.419

So the standard deviation is 0.419=0.6419mg/dI

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Most popular questions from this chapter

The chapter-opening Case Study described research by Teresa Amabile investigating whether external rewards would promote creativity in children’s artwork. Dr. Amabile conducted another study involving college students, who were divided into two groups using a chance process (like drawing names from a hat). The students in one group were given a list of statements about external reasons

(E) for writing, such as public recognition, making money, or pleasing their parents. Students in the other group were given a list of statements about internal reasons (I) for writing, such as expressing yourself and

enjoying playing with words. Both groups were then instructed to write a poem about laughter.

Each student’s poem was rated separately by 12different poets using a creativity scale. The 12poets’ ratings of each student’s poem were averaged to obtain an overall creativity score.

A dot-plot of the two groups’ creativity scores is shown below. Compare the two distributions. What do you conclude about whether external rewards promote creativity?

Comparing car colours Favorite vehicle colours may differ among types of vehicles. Here are data on the most popular colours in 2008 for luxury cars and for SUVs, trucks, and vans.

(a) Make a graph to compare colours by vehicle type.

(b) Write a few sentences describing what you see.

The mean salary of all female workers is \(35,000 The mean salary of all male workers is \)41,000 What must be true about the mean salary of all workers?

(a) It must be \(38,000

(b) It must be larger than the median salary.

(c) It could be any number between \)35,000 and \(41,000

(d) It must be larger than \)38,000

(e) It cannot be larger than $40,000

At the Census Bureau Web site, you can view detailed data collected by the American Community Survey. The table below includes data for 10 people chosen at random from the more than one million people in households contacted by the survey. “School” gives the highest level of education completed.

This data set contains

(a) 7 variables, 2 of which are categorical.

(b) 7 variables, 1 of which is categorical.

(c) 6 variables, 2 of which are categorical.

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(e) None of these.

Which of the following bar graphs is equivalent to the pie chart in Question T1.2?
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