Question

The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. Find the mean, median, mode, and standard deviation. Round to one decimal place as needed.19, 22, 25, 28, 29, 32, 34, 34Mean = Median = Mode = Standard Deviation = 6.8

Answer 1

First, let's calculate the mean.

The mean is the average, which is the sum of each term and then divide it by the number of samples:

`mean=(19+22+25+28+29+32+34+34)/(8)=27.9`

Now, the median is the central value of the dataset when it is listed in order from lower to higher:

`19,22,25,(28,29),32,34,34`

In this case, there is two central numbers -there is 3 numbers remaining on the right and 3 on the left-, namely 28 and 29, hence the median is calculated as the average, which is 28.5.

Next, the mode is the value which appears more often in the dataset. In this case there is two "34", hence the mode is 34.

Finally the standar deviation formula:

`\sqrt{\frac{\sum_{n\mathop{=}1}^8|x-u|^2}{N-1}}`

Where x is each value of the dataset, u is the mean, N the number of data. In this case:

Hence the answer is, mean=27.9, median=28.5, mode=34, standard deviation=5.5