Question

question 38
the mode is similar to the median as a measure of central tendency in that
its value must correspond to an actual score in the data set
it balances the distance between scores above and below its value
it represents the middle of a distribution
there are no symbols used to differentiate between whether its value(s) pertains to populations or samples
question 39
a sample has n = 6 scores: 1, 1, 3, 4, 6, and 8. the median for this sample is 3.5.
true
false

Explanation:

Step1: Recall mode and median definitions

Mode is most frequent value, median is middle - value. Both are actual scores in data set when data is discrete.

Step2: Analyze each option for Question 38

• Option 1: Correct. Both mode and median are actual scores in data set.
• Option 2: This is property of mean, not mode/median.
• Option 3: This is property of median (balance point in a sense), not mode.
• Option 4: Mode is about frequency, not middle - of - distribution like median.
• Option 5: There are symbols for population and sample for both ($M_o$ for mode, $\tilde{x}$ for sample median, $\widetilde{\mu}$ for population median in some cases).

Step3: Calculate median for Question 39

Arrange data in ascending order: 1, 1, 3, 4, 6, 8. Since $n = 6$ (even), median is average of $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values. $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$. The 3rd value is 3 and 4th value is 4. Median=$\frac{3 + 4}{2}=3.5$.

Answer:

Question 38: its value must correspond to an actual score in the data set
Question 39: True