Question

A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The strength of concrete is measured by pouring the mix into casting cylinders 6 inches in diameter and 12 inches tall. The concrete is allowed to set for 28 days. The concrete’s strength is then measured. The following data represent the strength of nine randomly selected casts (in psi). 3960, 4090, 3200, 3100, 2940, 3830, 4090, 4040, 3780 Compute the mean, median, and mode strength of the concrete (in psi).

Answer 1

Answer:

a) Mean = 3670

b) Median = 3830

c) Mode = 4090

Step-by-step explanation:

a) By mean, we imply the average of the sample collected. This is given by the formula:

Mean ($\bar{x}$) = $\frac{\sum\limits_{i=1}^{n}{x}}{n}$, where n is the sample size and x is the samples collected.

==> $\bar{x}$ = (2940+3100+3200+3780+3830+3960+4040+4090+4090 )/9

==> $\bar{x}$  = 33030/9 = 3670

b) By median, we imply middle value. Since the data size is small, we can easily sort the data in ascending or descending order. Then, we pick the middle value.

Sorted value => 2940 3100 3200 3780 3830 3960 4040 4090 4090

By formula, median = ((n+1)/2)th = 5th position value.

Therefore, the median = 3830

c) By mode, we imply the most occurrence value in the dataset. From the sorting: 2940 3100 3200 3780 3830 3960 4040 4090 4090 ,

The last two values occur most. Therefore, the mode is:

===> 4090