Question

McGraw-Connect Math Demine whether the Automotive emissions: Following are levels of particulate emissions for 30 vehicles driven at sea level and for 30 vehicles driven de at high altitude. Sea Level 1.3 3.5 1.1 1.1 0.9 1.3 0.9 0.6 1.3 2.5 1.5 1.1 1.1 2.2 0.9 1.8 1.5 1.2 1.6 6.6 4.0 2.5 1.4 1.4 1.8 1.1 1.6 3.7 0.6 2.7 High Altitude 4.4 3.8 2.4 3.8 5.3 5.8 2.9 4.7 1.9 9.1 8.7 9.5 2.7 9.2 7.3 2.1 6.3 6.5 6.3 2.0 5.9 5.6 5.6 1.5 6.5 5.3 5.6 2.1 1.1 3.3 Send data Part: 0/6 Part 1 of 6 (a) Find the median, the first quartile, and the third quartile of the sea-level emissions The median of the sea-level emission is The first quartile of the sea-level emission is The third quartile of the sea-level emission is Submit Assignme Next Part 2020 M. Education. All Rights Reserved. Terms of Use

Answer 1

a. 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:

0.6   0.6   0.9   0.9   0.9   1.1   1.1   1.1   1.1   1.1   1.2   1.3   1.3   1.3   1.4   1.4   1.5   1.5   1.6   1.6   1.8   1.8   2.2   2.5   2.5   2.7   3.5   3.7   4   6.6   

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 is $\frac{1.4+1.4}{2}=1.4$

b. 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.

0.6   0.6   0.9   0.9   0.9   1.1   1.1   1.1   1.1   1.1   1.2   1.3   1.3   1.3   1.4   1.4   1.5   1.5   1.6   1.6   1.8   1.8   2.2   2.5   2.5   2.7   3.5   3.7   4   6.6   

So, the bottom half is

0.6   0.6   0.9   0.9   0.9   1.1   1.1   1.1   1.1   1.1   1.2   1.3   1.3   1.3   1.4   

The median of these numbers is 1.1.

c. The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

0.6   0.6   0.9   0.9   0.9   1.1   1.1   1.1   1.1   1.1   1.2   1.3   1.3   1.3   1.4   1.4   1.5   1.5   1.6   1.6   1.8   1.8   2.2   2.5   2.5   2.7   3.5   3.7   4   6.6   

So, the upper half is

1.4   1.5   1.5   1.6   1.6   1.8   1.8   2.2   2.5   2.5   2.7   3.5   3.7   4   6.6   

The median of these numbers is 2.2.