Question

A supermarket is testing brands of microwave popcorn. For each brand, they recorded the percentage of corn kernels in a package that popped in the recommended cooking time. Let A be the data set of percentages listed below. A = 91, 94, 89, 93, 87, 92, 86, 87, 92, 91 The supermarket then realized they missed a brand. When the new brand was cooked, only 74% of its kernels popped. Let B be the data set of percentages for all 11 packages, including the package where the least kernels popped. Select the statements that are true. Including the percentage for the package where the least kernels popped causes the center of the data to increase. *Select all the correct answers. 1.) The mean of A is the same as the mean of B. 2.) The standard deviation of B is greater than the standard deviation of A. 3.) The interquartile range of A is the same as the interquartile range of B. 4.) The median of A is the same as the median of B. 5.)

Including the percentage for the package where the least kernels popped causes the center of the data to increase.

Select all the correct answers.
The mean of A is the same as the mean of B.
The standard deviation of B is greater than the standard deviation of A.
The interquartile range of A is the same as the interquartile range of B.
The median of A is the same as the median of B.
Including the percentage for the package where the least kernels popped causes the spread of the data to decrease.

Answer 1

The mean of dataset A is not the same as dataset B after adding a lower value. The standard deviation of B is indeed greater than that of A due to increased variability. The median may change and thus not remain the same and adding a lower value to the dataset decreases the center, not increases it.

Step-by-step explanation:

When considering the statements about the data sets A and B, where A consists of data points 91, 94, 89, 93, 87, 92, 86, 87, 92, 91 and B is the same as A with an additional data point of 74, the properties of the datasets can be analysed.

The mean for dataset A is not the same as for dataset B because adding a lower value, such as 74, would decrease the overall average. Thus, statement 1 is false. Statement 2 states that the standard deviation of B is greater than the standard deviation of A, which is true because the new value, 74, is more spread out from the mean, causing more variation. The interquartile range (IQR) for the sets may or may not be the same because the IQR concerns the middle 50% of the data, which might remain the same depending on the quartiles. Statement 4, regarding the median, is not necessarily true; adding another data point can change the position of the median. Finally, statement 5 regarding the claim that including the least percentage increases the center of the data is false; it actually decreases the center.