Question

A normal curve is a smooth curve that is symmetric and beil shaped. Data distributions that are mound

shaped are often modeled using a normal curve, and we say that such a distribution is approximately
normal. One example of a distribution that is approximately normal is the distribution of company heights
from example 1. Distributions that are approximately normal occur in many different settings. For example,
a salesman kept track of the gas mileage for his car over a 25-week span. The mileages (miles per gallon
rounded to the nearest whole number) were
23, 27, 27, 28, 25, 26, 25, 29, 26, 27, 24, 26, 26, 24, 27, 25, 28, 25, 26, 25, 29, 26, 27, 24, 26
a. Find the mean and the standard deviation of the mileage data."

Answer 1

The mean of the mileage data is approximately 25.48. The standard deviation of the mileage data is approximately 1.30.

Step-by-step explanation:

To find the mean of the mileage data, we add up all the values and divide by the total number of values. So for the given data set, the mean is calculated as:

Mean = (23 + 27 + 27 + 28 + 25 + 26 + 25 + 29 + 26 + 27 + 24 + 26 + 26 + 24 + 27 + 25 + 28 + 25 + 26 + 25 + 29 + 26 + 27 + 24 + 26) / 25 \approx 25.48

To find the standard deviation, we need to first find the variance. The variance is the average of the squared deviations from the mean. Then, we take the square root of the variance to get the standard deviation. So for the given data set, the standard deviation is:

Standard Deviation = sqrt(((23-25.48)^2 + (27-25.48)^2 + (27-25.48)^2 + ... + (24-25.48)^2) / 25) \approx 1.30