Question

1. which statement is true about these 2 distributions?

set a
set b

a. the mean of set a is less than the mean of set b, and their standard deviations are the same.
b. the mean of set a is greater than the mean of set b, and their standard deviations are the same.
c. the standard deviation of set a is less than the standard deviation of set b, and their means are the same.
d. the standard deviation of set a is greater than the standard deviation of set b, and their means are the same.

1. mai collects information about 37 classmates. she believes her data set is perfectly symmetrical with a mean and median of 20. she then realizes that the number she has recorded as 32 was actually supposed to be 42. what is true about the mean and median of her corrected data set?

a. the mean and median of the corrected set are both still 20.
b. the mean of the corrected data set is still 20, but the median is greater than 20
c. the median of the corrected data set is still 20, but the mean is greater than 20.
d. the mean and median of the corrected set are both greater than 20.
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Explanation:

Question 1

To determine the correct statement, we analyze the mean and standard deviation of set A and set B.

• Mean Analysis: The mean represents the center of the data. By visually inspecting the dot plots, the overall center (mean) of both sets appears to be similar (since the distribution of dots is symmetrically centered around the same value when considering the spread and peak).
• Standard Deviation Analysis: Standard deviation measures the spread of data. Set A has a dot at 7, which is further from the center than any data point in set B. This means set A has a wider spread (greater standard deviation) than set B.

Thus, the means are the same, and the standard deviation of set A is greater than that of set B, matching option d.

• Median: The median is the middle value (or average of middle values) in a sorted data set. Changing one value (from 32 to 42) does not affect the position of the middle value (since the data set has 37 values, the 19th value remains the same). Thus, the median stays 20.
• Mean: The mean is the sum of values divided by the number of values. Since we increased a value from 32 to 42, the total sum increases by \( 42 - 32 = 10 \). A larger sum with the same number of values (37) means the mean will be greater than 20.

This matches option c.

Answer:

d. The standard deviation of set A is greater than the standard deviation of set B, and their means are the same.

Question 2