select the correct answer.

what is the difference between the mean and the median of the following distribution?

\{1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9\}

0.17
0.19
0
0.26

Question

select the correct answer.

what is the difference between the mean and the median of the following distribution?

\{1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9\}

0.17
0.19
0
0.26

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Mean and Median", "Statistical Difference" ], "current_concepts": [ "Mean and Median", "Statistical Difference" ] } ## Calculate the mean of the distribution $$ \begin{aligned} \text{Data set: } & \{1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9\} \ N = & 21 \ \sum x = & (1 \times 3) + (2 \times 4) + (3 \times 2) + (4 \times 4) + (5 \times 2) + 6 + (7 \times 2) + (8 \times 2) + 9 \ = & 3 + 8 + 6 + 16 + 10 + 6 + 14 + 16 + 9 = 88 \ \text{Mean } (\mu) = & \frac{88}{21} \approx 4.1905 \end{aligned} $$ ## Find the median of the distribution $$ \begin{aligned} \text{Position of median} = & \frac{21 + 1}{2} = 11\text{th value} \ \text{Ordered values: } & 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, \mathbf{4}, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9 \ \text{Median } (M) = & 4 \end{aligned} $$ ## Calculate the difference between the mean and the median $$ \begin{aligned} \text{Difference} = & |\mu - M| \ = & |4.1905 - 4| \ = & 0.1905 \approx 0.19 \end{aligned} $$

(A) 0.17

(B) 0.19

(C) 0

(D) 0.26

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Mean and Median" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the mean of the distribution

Find the median of the distribution

Calculate the difference between the mean and the median

Answer: