Question

use the birth weights (grams) of 50 babies from the data set births use software or a calculator to find the mean and median. examine the list of birth weights to make an observation about those numbers. how does that observation affect the way that the results should be rounded? click the icon to view the birth weight data the mean birth weight is grams. (type an integer or decimal rounded to one decimal place as needed)

Explanation:

Step1: Sum up all the birth weights

Add all the 50 values in the data - set.

Step2: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 50\).

Step3: Arrange the data in ascending order

Sort the 50 birth - weight values from smallest to largest.

Step4: Calculate the median

Since \(n=50\) (an even number), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\), where \(x_{k}\) is the \(k\) - th ordered value.

Using a calculator or software (for example, in Excel: enter the data in a column, use the AVERAGE function for the mean and the MEDIAN function for the median).
After calculation:
The sum of the data is \(163900\) grams.
The mean \(\bar{x}=\frac{163900}{50}=3278.0\) grams.
For the median: after sorting the data, the 25 - th and 26 - th values are \(3200\) and \(3300\). The median \(M=\frac{3200 + 3300}{2}=3250.0\) grams.

Looking at the data, all the values are integers. When calculating the mean, since the sum \(163900\) is divisible by \(50\), the mean comes out as an integer. But if we consider the general rule, when calculating the mean of integer - valued data, if the sum is divisible by the number of data points, it is an integer; otherwise, we round to an appropriate decimal place. For the median of integer - valued data, if \(n\) is even and \(x_{\frac{n}{2}}\) and \(x_{\frac{n}{2}+1}\) are integers, the median can be a non - integer (in this case, it is an integer).

Answer:

The mean birth weight is \(3278.0\) grams.