MAT201- FALL II 2017 - Shaw Quiz: Module 2 Quiz This Question: 5 pts 4017 (1 com
ID: 3356288 • Letter: M
Question
MAT201- FALL II 2017 - Shaw Quiz: Module 2 Quiz This Question: 5 pts 4017 (1 complete) The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine. 1 MPG Data (a) Compute the z-score corresponding to the individual who obtained 49.0 miles per gallon. Interpret this result (b) Determine the quartiles. ) Compute and interpret the interquartile range, IQR (d) Determine the lower and upper fences Are there any outliers? Click the icon to view the data. 6- 40.2-425 36.2 37.9 38.9 40.6 42.9 34.6 37.3 38.0 39 1 414 43.7 (a) Compute the z-score corresponding to the individual who obtained 49.0 miles per gallon Interpret this result 4 39.8 41 The z-score corresponding to the individual is and indicates that the data value is (Type integers or decimals rounded to two decimal places as needed) standard deviation s the Print Done (b) Determine the quartiles Type an integer or a decimal. Do not round) (Type an integer or a decimal Do not round.) (Type an integer or a decimal. Do not round) mpg (c) Compute and interpret the interquartile range IQR Select the correct choice below and ill in the answer box to complete your choice (Type an integer or a decimal. Do not round ) A. The interquartile range ismpg It is the range of all of the observations in the data set O B. The interquartile range is mpg It is the range of the observations between the lower and upper fences c. The interquarti e range is mpg. It is the range of the observations between either the lower or upper quan le and the middle quartile it captures 25% of the observations 0 D. The interquartile range is 1 mpg It is the range of the middle 50% of the observations in the data set Click to select your answer(s) 0 Type here to searchExplanation / Answer
Solution:- given that 32.3 35.8 37.8 38.6 40.2 42.5 34.3 36.2 37.9 38.9 40.6 42.9 34.6 37.3 38.0 39.1 41.4 43.7 35.4 37.5 38.4 39.8 41.6 49.0
mean = 38.91, = 3.57
a) The z score corresponding to the individual is 49 and indicates that the data value is 3.57 standard deviation(s) above the mean.
z score = (X - mu)/
= (49 - 38.91)/3.57 = 2.83
b)
==> Q1 = 36.75 mpg
Explanation
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.
32.3 34.3 34.6 35.4 35.8 36.2 37.3 37.5 37.8 37.9 38.0 38.4 38.6 38.9 39.1 39.8 40.2 40.6 41.4 41.6 42.5 42.9 43.7 49.0
So, the bottom half is
32.3 34.3 34.6 35.4 35.8 36.2 37.3 37.5 37.8 37.9 38.0 38.4
The median of these numbers is 36.75.
==> Q2 = 38.5 mpg
Explanation
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
32.3 34.3 34.6 35.4 35.8 36.2 37.3 37.5 37.8 37.9 38.0 38.4 38.6 38.9 39.1 39.8 40.2 40.6 41.4 41.6 42.5 42.9 43.7 49.0
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median = (38.4+38.6)/2 = 38.5
==> Q3 = 41 mpg
c)
The interquartile range of the data set is 4.25.
Explanation
The interquartile range is the difference between the third and first quartiles.
The third quartile is 41.
The first quartile is 36.75.
The interquartile range = 41 - 36.75 = 4.25.
option A. The inter quartile range is 4.25. mpg it is the range of all the observation in the data set
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