Percent Obese by State Computer output giving descriptive statistics for the percent of the population that is obese for each of the 50 US states, from the USStates dataset, is given in the table shown below. Since all 50 US states are included, this is a population, not a sample. Descriptive Statistics: Obese Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Obese 50 0 28.766 0.476 3.369 21.300 26.375 29.400 31.150 35.100 Percent of the population that is obese by state Click here for the dataset associated with this question. Condition gt requires numbers instead of "null" and "0" (a) What are the mean and the standard deviation? μ=% σ=% (b) Calculate the z-score for the largest value and interpret it in terms of standard deviations. Do the same for the smallest value. Round your answers to three decimal places. The largest value: z-score= The maximum of 35.1% obese is standard deviations abovebelow the mean. The smallest value: z-score= The minimum of 21.3% obese is standard deviations abovebelow the mean. Condition gt requires numbers instead of "null" and "0" (c) This distribution is relatively symmetric and bell-shaped. Give an interval that is likely to contain about 95% of the data values. Round your answers to three decimal places. The interval is: % to %.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 3BGP

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Percent Obese by State

Computer output giving descriptive statistics for the percent of the population that is obese for each of the 50 US states, from the USStates dataset, is given in the table shown below. Since all 50 US states are included, this is a population, not a sample.

Descriptive Statistics: Obese
Variable	N	N*	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum
Obese	50	0	28.766	0.476	3.369	21.300	26.375	29.400	31.150	35.100

Percent of the population that is obese by state

Click here for the dataset associated with this question.

Condition gt requires numbers instead of "null" and "0"

(a) What are the mean and the standard deviation?

μ=%

σ=%

(b) Calculate the z-score for the largest value and interpret it in terms of standard deviations. Do the same for the smallest value.

Round your answers to three decimal places.

The largest value:

z-score=

The maximum of 35.1% obese is standard deviations

abovebelow

the mean.

The smallest value:

z-score=

The minimum of 21.3% obese is standard deviations

abovebelow

the mean.

Condition gt requires numbers instead of "null" and "0"

(c) This distribution is relatively symmetric and bell-shaped. Give an interval that is likely to contain about 95% of the data values.

Round your answers to three decimal places.

The interval is: % to %.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

Z score is a statistical term that measures the relationship between mean and standard deviation. For maximum/minimum value we calculate the z-score using the formula,

$z = \frac{m a x o r m i n v a l u e - μ}{σ}$

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