Question

select the correct answer from each drop - down menu. the table shows the heights of the 10 tallest buildings in san francisco and los angeles. heights of tallest buildings in san francisco (meters) heights of tallest buildings in los angeles (meters) 260 310 237 262 212 229 197 228 184 224 183 221 183 220 175 219 174 213 173 213 the average height of the 10 tallest buildings in los angeles is than the average height of the tallest buildings in san francisco. the mean absolute deviation for the 10 tallest buildings in san francisco is

Explanation:

Step1: Calculate San Francisco average

Sum heights and divide by 10. \( \bar{x}_{SF}=\frac{260 + 237+212 + 197+184+183+183+175+174+173}{10}=198.8\)

Step2: Calculate Los Angeles average

Sum heights and divide by 10. \( \bar{x}_{LA}=\frac{310+262 + 229+228+224+221+220+219+213+213}{10}=236.9\)

Step3: Compare averages

Since \(236.9>198.8\), Los Angeles has a greater average.

Step4: Calculate San Francisco MAD

Find absolute - deviations from mean, sum them, divide by 10. \(MAD_{SF}=\frac{\sum_{i = 1}^{10}|x_{i}-\bar{x}_{SF}|}{10}\), where \(x_{i}\) are the individual heights.

Answer:

1. First, find the average height of buildings in San Francisco:

• The sum of the heights of the 10 tallest buildings in San Francisco is \(260 + 237+212 + 197+184+183+183+175+174+173=1988\).
• The average height \( \bar{x}_{SF}=\frac{1988}{10}=198.8\) meters.

1. Then, find the average height of buildings in Los - Angeles:

• The sum of the heights of the 10 tallest buildings in Los Angeles is \(310+262 + 229+228+224+221+220+219+213+213 = 2369\).
• The average height \( \bar{x}_{LA}=\frac{2369}{10}=236.9\) meters.
• Since \(236.9>198.8\), the average height of the 10 tallest buildings in Los Angeles is greater than the average height of the 10 tallest buildings in San Francisco.

1. Next, find the mean - absolute deviation (MAD) for the 10 tallest buildings in San Francisco:

• Calculate the absolute deviations from the mean:
• \(|260 - 198.8|=61.2\), \(|237 - 198.8| = 38.2\), \(|212-198.8| = 13.2\), \(|197 - 198.8|=1.8\), \(|184 - 198.8| = 14.8\), \(|183 - 198.8|=15.8\), \(|183 - 198.8| = 15.8\), \(|175 - 198.8|=23.8\), \(|174 - 198.8| = 24.8\), \(|173 - 198.8|=25.8\).
• The sum of the absolute deviations is \(61.2+38.2 + 13.2+1.8+14.8+15.8+15.8+23.8+24.8+25.8 = 235.8\).
• The mean - absolute deviation \(MAD_{SF}=\frac{235.8}{10}=23.58\) meters.

So, the average height of the 10 tallest buildings in Los Angeles is greater than the average height of the tallest buildings in San Francisco. The mean absolute deviation for the 10 tallest buildings in San Francisco is \(23.58\) meters.