The 152 heights of males from a data set of body measurements vary from a low of 157.0 cm to a high of 191.9 cm. Use the range rule of thumb to estimate the standard deviation s and compare the result to the standard deviation of 7.99 cm calculated using the 152 heights. What does the result suggest about the accuracy of estimates of s found using the range rule of thumb? Assume the estimate is accurate if it is within 1.3 cm.

Answers

Answer 1

The estimate is considered accurate if it is within 1.3 cm, or 8.72 cm, as indicated by the results about the accuracy of estimates of s discovered using the range rule of thumb.

What a standard deviation means?

While a high standard deviation indicates that the data are much more spread, a small standard deviation suggests that the data are clustered around the mean. The standard deviation is a measure of how variable your data set is on average. It displays the standard deviation of the each score with respect to the mean.

Why standard deviation is used and how should calcite it?

Standard deviation is important because it makes measurements easier to understand when the data is dispersed. The more equally distributed the data is, the bigger overall standard deviation of a data will be.

Determine the mean first. Step 2: Determine the square of the variation from the mean of each data point. In Step 3, add the values from Step 2. By the overall amount of information collected in step 4, divide.

The range rule of thumb is a rough estimation of a data set's standard deviation based on the data's range. The estimate comes from:

s ≈ R / 4

where R denotes the data range, which is the difference between the data set's maximum and minimum values. The guys' heights in this instance range from 191.9 to 157.0 cm, or 34.9 cm.

We estimate the standard deviation to be as follows using the range rule of thumb:

s ≈ 34.9 / 4 = 8.72 cm

We can observe that the estimate is within 1.3 cm of the real standard deviation by comparing it to the estimated standard deviation, which is 7.99 cm. This shows that the standard deviation estimate derived from the range rule of thumb is rather accurate.

It is important to remember that this rule of thumb is only a rough estimate, and that there are more exact ways to get the standard deviation, such as the calculation based on the mean and variance, which should be used in most situations.

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Related Questions

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Answer:

Explanation:

Answer:

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Step-by-step explanation:

Which of the following best describes the mission of the X-1 aircraft based on hidden figures

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The X-1 aircraft's mission is based on To put a man on the moon, travel at the speed of light, and launch an aeroplane into space

What purpose is the basis for Hidden Figures?

The latest box office sensation Hidden Figures (2017) sheds light on the previously mostly untold tale of the women who worked as computers on NASA's Project Mercury in the 1960s. The main three actors in the film are Taraji P. Henson, Janelle Monáe, and Octavia Spencer.

What aspect of Hidden Figures is the best?

When the women's car breaks down on the way to Langley Research Center and a police comes up asking for identification, Katherine hands him her card and murmurs seriously, "NASA, sir," in one of Hidden Figures' greatest scenes.

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x^2+10 = 91
What is the positive solution to the given equation?

Answers

To solve this problem, we will factor.
x^2+10=91
Subtract 91 to both sides:
x^2+10-91=0
Calculate:
x^2-81=0
Factor:
(x+9)(x-9)=0
Separate:
x+9=0
x-9=0
Solve:
x=-9
x=9
The positive solution is x=9
Hope this helped!

Answer:

Explanation:

To find the positive solution to the equation x^2 + 10 = 91, we'll start by isolating x^2 on one side of the equation. To do this, we'll subtract 10 from both sides:

x^2 + 10 - 10 = 91 - 10

x^2 = 81

Next, we'll take the square root of both sides of the equation to solve for x:

√(x^2) = √(81)

x = ±9

Since we are looking for the positive solution, x = 9.

The following data,
11,16,10,30,24,5,6,12,11,45,9,8,3,4,35,31,
represents the
number of days spent by COVID 19 patients admitted at the
Intensive Care Unit of the University of Ghana Medical
Centre. Find
1. the mean
2. range
3. interquartile range
4. variance and standard deviation
5. the coefficient of variation.
6. Comment on your results

Answers

Answer:

Explanation:

Here are the results for the data:

Mean: The mean, or average, of the data can be calculated by summing up all the values and dividing by the number of values:

(11+16+10+30+24+5+6+12+11+45+9+8+3+4+35+31)/16 = 201/16 = 12.5625

So, the mean number of days spent by COVID-19 patients in the ICU is 12.5625 days.

Range: The range of the data is the difference between the maximum and minimum values:

45 - 3 = 42

So, the range of the data is 42 days.

Interquartile Range: The interquartile range (IQR) is a measure of the dispersion of the data that is less sensitive to outliers than the range. To calculate the IQR, we first need to find the median (Q2), first quartile (Q1), and third quartile (Q3) of the data:

Q1 = (6+8)/2 = 7

Q2 = (11+12)/2 = 11.5

Q3 = (24+30)/2 = 27

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1 = 27 - 7 = 20

Variance and Standard Deviation: Variance is a measure of the dispersion of the data that is used to calculate the standard deviation. The formula for variance is:

Variance = sum of squared deviations from the mean / number of values

First, we need to calculate the deviations from the mean:

11 - 12.5625 = -1.5625

16 - 12.5625 = 3.4375

10 - 12.5625 = -2.5625

...

The sum of the squared deviations from the mean is:

Variance = 596.9375/16 = 37.93359375

The standard deviation is the square root of the variance:

Standard deviation = √Variance = √37.93359375 = 6.15

Coefficient of Variation: The coefficient of variation (CV) is a measure of the relative variability of the data, expressed as a percentage of the mean. The formula for the CV is:

CV = (Standard deviation / mean) * 100

CV = (6.15 / 12.5625) * 100 = 49.03%

Comment on Results:

The mean number of days spent by COVID-19 patients in the ICU at the University of Ghana Medical Centre is 12.5625 days. The range of the data is 42 days, while the interquartile range is 20 days. The variance is 37.93 and the standard deviation is 6.15. The coefficient of variation is 49.03%, which indicates a relatively high degree of variability in the data. These results show that the number of days spent by COVID-19 patients in the ICU at the University of Ghana Medical Centre can vary widely, with some patients spending as few as 3 days and others spending as many as 45 days in the ICU.

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