Question

1. two data sets are given:

data set a: 2, 4, 6, 8, 10
data set b: 1, 3, 5, 7, 9
which statement correctly compares the two data sets?
a. data set b has a higher mean than data set a.
b. data set b has a larger median than data set a.
c. data set a and data set b have the same range.
d. data set a has more variability than data set b.

Explanation:

Step1: Calculate mean for both data sets

For Data Set A: Mean = $\frac{2 + 4 + 6 + 8 + 10}{5}=\frac{30}{5} = 6$
For Data Set B: Mean = $\frac{1 + 3 + 5 + 7 + 9}{5}=\frac{25}{5}=5$
So option a is wrong.

Step2: Calculate median for both data sets

Data Set A (sorted): 2, 4, 6, 8, 10. Median is the middle value, 6.
Data Set B (sorted): 1, 3, 5, 7, 9. Median is the middle value, 5.
So option b is wrong.

Step3: Calculate range for both data sets

Range = Maximum - Minimum
Data Set A: $10 - 2 = 8$
Data Set B: $9 - 1 = 8$
So their ranges are equal.

Step4: Check variability (using range as a measure)

Since both have the same range, their variabilities (in terms of range) are equal. So option d is wrong.

Answer:

c. Data Set A and Data Set B have the same range.