using technology to analyze symmetry and skew\nenter each data set into the statistics calculator. make note…

using technology to analyze symmetry and skew\nenter each data set into the statistics calculator. make note of the mean, median, and shape of the histogram of each data set.\na = {10, 12, 12, 6, 8, 5, 4, 10, 8, 10, 12, 12, 6}\nb = {8, 8, 8, 7, 9, 7, 9, 10, 6, 8}\nwhich statements are true about the data sets? check all that apply.\nset a is symmetrical.\nset b has the same mean and median.\nset b is right skewed.\nset a is left skewed.\nthe median of set a is larger than the mean of set a.

using technology to analyze symmetry and skew\nenter each data set into the statistics calculator. make note of the mean, median, and shape of the histogram of each data set.\na = {10, 12, 12, 6, 8, 5, 4, 10, 8, 10, 12, 12, 6}\nb = {8, 8, 8, 7, 9, 7, 9, 10, 6, 8}\nwhich statements are true about the data sets? check all that apply.\nset a is symmetrical.\nset b has the same mean and median.\nset b is right skewed.\nset a is left skewed.\nthe median of set a is larger than the mean of set a.

Answer

Answer:

  1. First, find the mean, median and shape for set A:
    • Mean of set A:
      • The sum of the data in set A: (10 + 12+12 + 6+8 + 5+4 + 10+8 + 10+12+12+6=\sum_{i = 1}^{13}x_{i}=115).
      • The number of data - points (n = 13).
      • The mean (\bar{x}A=\frac{\sum{i = 1}^{13}x_{i}}{n}=\frac{115}{13}\approx8.85).
      • To find the median, arrange the data in ascending order: (4,5,6,6,8,8,10,10,10,12,12,12,12). Since (n = 13) (odd), the median (M_A) is the (\left(\frac{n + 1}{2}\right)) - th value, i.e., the 7 - th value. So (M_A = 10).
      • Since the mean ((\approx8.85)) is less than the median ((10)), set A is left - skewed.
    • Mean of set B:
      • The sum of the data in set B: (8 + 8+8 + 7+9 + 7+9 + 10+6 + 8=\sum_{i = 1}^{10}x_{i}=78).
      • The number of data - points (n = 10).
      • The mean (\bar{x}B=\frac{\sum{i = 1}^{10}x_{i}}{n}=\frac{78}{10}=7.8).
      • To find the median, arrange the data in ascending order: (6,7,7,8,8,8,8,9,9,10). Since (n = 10) (even), the median (M_B=\frac{8 + 8}{2}=8).
      • Since the mean ((7.8)) is less than the median ((8)), set B is left - skewed.
  2. Analyze each statement:
    • Set A is symmetrical: False, since set A is left - skewed.
    • Set B has the same mean and median: False, as (\bar{x}_B = 7.8) and (M_B = 8).
    • Set B is right - skewed: False, set B is left - skewed.
    • Set A is left - skewed: True.
    • The median of set A is larger than the mean of set A: True, since (M_A = 10) and (\bar{x}_A\approx8.85).

So the true statements are: Set A is left - skewed; The median of set A is larger than the mean of set A.

Explanation:

Step1: Calculate mean of set A

Sum data values and divide by (n = 13).

Step2: Calculate median of set A

Arrange data and find middle value.

Step3: Determine skew of set A

Compare mean and median.

Step4: Calculate mean of set B

Sum data values and divide by (n = 10).

Step5: Calculate median of set B

Arrange data and find average of two middle values.

Step6: Determine skew of set B

Compare mean and median.

Step7: Evaluate statements

Check each statement against calculated values.