Question

The histograms below summarize the average travel time to work for random samples of 70 workers in the los angeles area and 61 workers in thr new york city area.

a) briefly compare the distribution of travel times for these two regions

b) suppose you wanted to make the point that typical travel time is longer in the new york city area than in the los angeles area. which measure of center would you use? justify your answer

Answer 1

Both the median and the 75th percentile suggest that typical travel times are longer in New York City than in Los Angeles. The 75th percentile may be a better choice in this case because it is less sensitive to the very long outliers in the New York City data.

The histograms show that the distribution of travel times is right-skewed for both Los Angeles and New York City. However, the New York City distribution appears to have a longer tail, indicating that there are more outliers with much longer travel times than in Los Angeles.

To make the point that typical travel time is longer in New York City, you could use the median or the 75th percentile. These measures are less sensitive to outliers than the mean, so they would be less likely to be pulled up by the few people with very long commutes in New York City.

The median is the travel time that divides the sample in half, so half of the people have commutes that are shorter than the median and half have commutes that are longer. The 75th percentile is the travel time that such that 75% of the people have commutes that are shorter and 25% have commutes that are longer.

In this case, the median travel time in Los Angeles is about 30 minutes, while the median travel time in New York City is about 40 minutes. The 75th percentile in Los Angeles is about 45 minutes, while the 75th percentile in New York City is about 60 minutes.

Answer 2

A) There are more workers in the L.A area that take up to 20 minutes to get to their job.

B)40 minutes or more.

Explanation:

Even though the graph from the New York area is more well distributed, you can see a clear increase in the number of cases above 40 minutes in the New York area compared to the Los Angeles, which are probable around 3o workes, while in the New York Area graph those travel times are reserved for more than half of the workers that were interviewed, so we can assure that workers from the New York Area spend more time traveling to their jobs.