Question

construct the described data set. the entries in the data set cannot all be the same.

the median and the mode are the same.

what is the definition of mode?

a. the data entry that is far removed from the other entries in the data set.
b. the sum of the data entries divided by the number of entries.
c. the data entry that occurs with the greatest frequency.
d. the value that lies in the middle of the data when the data set is ordered.

choose the data set where the median and mode of the set are equal.

a. 4, 4, 4, 5, 6, 6, 6
b. 1, 1, 7, 7, 7, 9, 9
c. 2, 4, 6, 8, 8, 10
d. 3, 3, 11, 11

a data set includes the entries 3, 4, 6, 8, 8, and 11. complete the data set with an entry between 1 and 11 so that the median and mode of the set are equal.

(type an integer or decimal.)

Explanation:

Define the mode of a data set

The mode is the data entry that occurs with the greatest frequency.

Analyze the given options for the second question

• Option A: \(4, 4, 4, 5, 6, 6, 6\). Modes are \(4\) and \(6\) (bimodal). Median is \(5\).
• Option B: \(1, 1, 7, 7, 7, 9, 9\). Mode is \(7\). Median is the middle value of \(7\) ordered entries, which is the \(4^{\text{th}}\) entry: \(7\). Thus, median = mode = \(7\).
• Option C: \(2, 4, 6, 8, 8, 10\). Mode is \(8\). Median is \(\frac{6+8}{2} = 7\).
• Option D: \(3, 3, 11, 11\). Modes are \(3\) and \(11\). Median is \(\frac{3+11}{2} = 7\).

Solve for the missing entry in the third question

Let the existing ordered data set be \(3, 4, 6, 8, 8, 11\) (size \(n = 6\)). The current mode is \(8\).
Let \(x\) be the added entry between \(1\) and \(11\). The new data set has size \(n = 7\).

• If \(x = 8\), the mode remains \(8\). The sorted set is \(3, 4, 6, 8, 8, 8, 11\). The median is the \(4^{\text{th}}\) value, which is \(8\). Here, median = mode = \(8\).

Answer:

Question 1

• A. The data entry that is far removed from the other entries in the data set.
• B. The sum of the data entries divided by the number of entries.
• C. The data entry that occurs with the greatest frequency. (Correct answer)
• D. The value that lies in the middle of the data when the data set is ordered.

Question 2

• A. 4, 4, 4, 5, 6, 6, 6
• B. 1, 1, 7, 7, 7, 9, 9 (Correct answer)
• C. 2, 4, 6, 8, 8, 10
• D. 3, 3, 11, 11

Question 3

A data set includes the entries 3, 4, 6, 8, 8, and 11. Complete the data set with an entry between 1 and 11 so that the median and mode of the set are equal.
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