Select all the correct answers.
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 spread of the data to decrease.
the mean of a is the same as the mean of b.
including the percentage for the package where the least kernels popped causes the center of the data to increase.
the median of a is the same as the median 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.