Question

enter each data set into the statistics calculator. make note of the mean, median, and shape of the histogram of each data set.
a = {10, 12, 12, 6, 8, 5, 4, 10, 8, 10, 12, 12, 6}
b = {8, 8, 8, 7, 9, 7, 9, 10, 6, 8}
which statements are true about the data sets? check all that apply.
set a is symmetrical.
set b has the same mean and median.
set b is right skewed.
set a is left skewed.
the median of set a is larger than the mean of set a.

Explanation:

Step1: Calculate mean and median for Set A

Sort Set A: \(4,5,6,6,8,8,10,10,10,12,12,12,12\)
Number of elements \(n = 13\)
Mean of Set A: \(\bar{x}_A=\frac{4 + 5+6+6+8+8+10+10+10+12+12+12+12}{13}=\frac{115}{13}\approx8.85\)
Median (middle - value, \(n = 13\), so \(7^{th}\) value) of Set A: \(10\)
Since the tail of the histogram (if we consider the distribution) is on the left side (smaller values \(4,5\)), Set A is left - skewed (\(mean

Step2: Calculate mean and median for Set B

Sort Set B: \(6,7,7,8,8,8,8,9,9,10\)
Number of elements \(n = 10\)
Mean of Set B: \(\bar{x}_B=\frac{6 + 7+7+8+8+8+8+9+9+10}{10}=\frac{80}{10}=8\)
Median (average of \(5^{th}\) and \(6^{th}\) values) of Set B: \(\frac{8 + 8}{2}=8\)
Since \(mean = median\), and the distribution is symmetric around the center (no long tail on either side)

Answer:

Set A is left - skewed, Set B has the same mean and median. So the correct statements are:

• Set B has the same mean and median.
• Set A is left skewed.