In automobile mileage and gasoline-consumption testing, 13...

In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance. $\begin{array}{lllllllllll}{\text { City: }} & {16.2} & {16.7} & {15.9} & {14.4} & {13.2} & {15.3} & {16.8} & {16.0} & {16.1} & {15.3} & {15.2} & {15.3} & {16.2} \\ {\text {Highway: }} & {19.4} & {20.6} & {18.3} & {18.6} & {19.2} & {17.4} & {17.2} & {18.6} & {19.0} & {21.1} & {19.4} & {18.5} & {18.7}\end{array}$ Use the mean, median, and mode to make a statement about the difference in performance for city and highway driving.

In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance.
$\begin{array}{lllllllllll}{\text { City: }} & {16.2} & {16.7} & {15.9} & {14.4} & {13.2} & {15.3} & {16.8} & {16.0} & {16.1} & {15.3} & {15.2} & {15.3} & {16.2} \\ {\text {Highway: }} & {19.4} & {20.6} & {18.3} & {18.6} & {19.2} & {17.4} & {17.2} & {18.6} & {19.0} & {21.1} & {19.4} & {18.5} & {18.7}\end{array}$
Use the mean, median, and mode to make a statement about the difference in performance for city and highway driving.

Key Concepts

Mean

Mean is a measure of central tendency calculated by summing all of the values in a dataset and dividing by the number of observations. It provides a concise summary of the overall performance of the automobiles by averaging all mileage values, giving insight into the general efficiency under the tested conditions.

Median

Median is the middle value of a dataset when the observations are arranged in order. It is a robust measure of central tendency that is less affected by extreme values than the mean, and it helps in understanding the typical performance by showing the central point of the distribution of mileage data.

Mode

Mode is the value that occurs most frequently in a dataset. It highlights the most common performance level among the automobiles tested and can indicate trends in driving conditions if certain mileage values appear repeatedly among the measurements.

Data Comparison

Data comparison involves using statistical measures like mean, median, and mode to analyze and contrast different conditions—in this case, city versus highway driving. By comparing these measures, one can determine how performance differs between the two scenarios, whether one consistently yields higher efficiency, and how the distribution of mileage values varies between them.

Transcript

00:01 This question is asking us to compare city driving to highway driving by comparing the mean, median, and mode of these two data sets.

00:09 Now, first off, let's remind ourselves how to find these three values.

00:15 For the mean, we want to take the sum of our data set and divide that by the number of data points that we have.

00:24 Now, for the median, we want our middle data point.

00:30 And to do that, we're going to have to order our data set from smallest to largest.

00:37 And finally, the mode is going to be our most frequent data point.

00:48 All right.

00:48 Now that we have that, let's get started with our city data.

00:57 First, we want to order our data set from smallest to largest.

01:02 So we have 13 .2, 14 .4, 15 .2, 15 .2, 15 .3, 15 .3.

01:12 15 .3, 15 .3, 15 .9, 16 .0, 16 .1, 16 .2, 16 .2, 16 .7.

01:30 And finally, 16 .8.

01:33 Now first, to find the mean, we're going to take the sum of these numbers.

01:38 So 13 .2, plus 14 .4.

01:40 And then to save space and time, i'm going to use this triple dot notation.

01:47 And we're going to divide by the number of data points we have, which in this case is 13.

01:51 Our sum is equal to 202 .6.

01:55 And when we divide that by 13, we get our mean to be 15 .6 miles per gallon.

02:03 Also note that i am rounding to the first decimal place because the values that are given to us are only to the first decimal place.

02:11 Next, we want to find the median.

02:16 Now, we already ordered our data set for ourselves from smallest to largest value.

02:20 Next, we can alternate in crossing out values from either end of this ordered list in order to find the middle value of this dataset.

02:31 And when we do that, we get that our median is 15 .9 miles per gallon.

02:40 And finally, to find our mode, we notice that we have the value 15 .4 .4.

02:45 Three times.

02:47 We also have the value 16 .2, two times, but three is greater than two.

02:52 So we have that our mode is going to be 15 .3 miles per gallon.

02:59 All right.

02:59 Now that we have that for our city data, we want to do the same thing, but with our highway data...

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