A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The concrete is poured into casting cylinders and 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). Compute the mean, median, and mode strength of the concrete (in psi).
3930
4060
3230
3090
2910
3800
4060
4040
3820
To solve this problem, we will first find the mean, median, and mode of the given data.
Mean: To find the mean, we need to sum up all the given values and divide by the total number of values.
Sum of the data = 3930 + 4060 + 3230 + 3090 + 2910 + 3800 + 4060 + 4040 + 3820 = 33440
Number of data points = 9
Mean = Sum of the data / Number of data points = 33440 / 9 = 3715.56 psi (rounded to the nearest hundredth)
Median: To find the median, we need to arrange the data in ascending order and find the middle value.
Arranging the data in ascending order: 2910, 3090, 3230, 3800, 3820, 3930, 4040, 4060, 4060
The middle value is the 5th value, which is 3820 psi.
Mode: The mode is the value or values that appear most frequently in the data.
From the given data, the value 4060 appears twice, which is more than any other value. Therefore, the mode of the data is 4060 psi.
To calculate the mean, median, and mode strength of the concrete, we will use the given data:
3930, 4060, 3230, 3090, 2910, 3800, 4060, 4040, 3820
Step 1: Calculate the Mean
The mean (or average) is calculated by summing all the data points and dividing it by the total number of data points.
Mean = (sum of all data points) / (total number of data points)
Mean = (3930 + 4060 + 3230 + 3090 + 2910 + 3800 + 4060 + 4040 + 3820) / 9
Mean = 35,140 / 9
Mean = 3904.44 psi
So, the mean strength of the concrete is approximately 3904.44 psi.
Step 2: Calculate the Median
The median is the middle value of a set of data when it is arranged in ascending order. First, we need to arrange the data in ascending order.
In ascending order: 2910, 3090, 3230, 3820, 3800, 3930, 4040, 4060, 4060
Since the total number of data points is odd, the median will be the value at the middle index:
Median = 3820
So, the median strength of the concrete is 3820 psi.
Step 3: Calculate the Mode
The mode is the value(s) that occur(s) most frequently in a set of data.
From the given data, we can observe that the value 4060 is repeated twice, which is more than any other value.
So, the mode of the concrete strength is 4060 psi.
Therefore, the mean, median, and mode strength of the concrete are as follows:
Mean strength: 3904.44 psi
Median strength: 3820 psi
Mode strength: 4060 psi