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: \(\bar{x}_A=\frac{4 + 5+6+6+8+8+10+10+10+12+12+12+12}{13}=\frac{125}{13}\approx9.62\)
Median (middle - value, \(n = 13\), so \(7^{th}\) value) of Set A: \(10\)
Since mean (\(\approx9.62\)) < median (\(10\)), Set A is left - skewed.

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 \( = 8\) and median \(=8\), Set B has the same mean and median. Also, since mean = median, Set B is symmetrical (not right - skewed)

Answer:

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