trade deficits (in billions of dollars)
country a 275.1 country l 67.4
country b 203.3 country m 42.9
country c 49.5 country n 33.4
country d 24.8 country o 26.1
country e 44.9 country p 40.3
country f 97.5 country q 31.6
country g 29.1 country r 15.6
country h 15.7 country s 10.1
country i 23.3
country j 14.1
country k 56.2

which measure of central tendency was affected more by the elimination of trade deficits to country a?

a. the mean was affected more than the median.
b. the median was affected more than the mean.
c. both the mean and the median were affected equally.

Question

trade deficits (in billions of dollars)
country a 275.1 country l 67.4
country b 203.3 country m 42.9
country c 49.5 country n 33.4
country d 24.8 country o 26.1
country e 44.9 country p 40.3
country f 97.5 country q 31.6
country g 29.1 country r 15.6
country h 15.7 country s 10.1
country i 23.3
country j 14.1
country k 56.2

which measure of central tendency was affected more by the elimination of trade deficits to country a?

a. the mean was affected more than the median.
b. the median was affected more than the mean.
c. both the mean and the median were affected equally.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mean Calculation", "Median Calculation", "Measures of Central Tendency Interpretation" ], "new_concepts": [], "current_concepts": [ "Mean Calculation", "Median Calculation", "Measures of Central Tendency Interpretation" ] } ## Calculate original and new mean values $$ \begin{aligned} &N_{\text{orig}} = 19 \ &\sum X_{\text{orig}} = 275.1 + 203.3 + 49.5 + 24.8 + 44.9 + 97.5 + 29.1 + 15.7 + 23.3 + 14.1 + 56.2 \ &\phantom{\sum X_{\text{orig}} =} + 67.4 + 42.9 + 33.4 + 26.1 + 40.3 + 31.6 + 15.6 + 10.1 = 1080.8 \ &\mu_{\text{orig}} = \frac{1080.8}{19} \approx 56.88 \ &N_{\text{new}} = 18 \ &\sum X_{\text{new}} = 1080.8 - 275.1 = 805.7 \ &\mu_{\text{new}} = \frac{805.7}{18} \approx 44.76 \ &|\Delta \mu| = |56.88 - 44.76| = 12.12 \end{aligned} $$ ## Calculate original and new median values $$ \begin{aligned} &\text{Sorted original (19 values): } 10.1, 14.1, 15.6, 15.7, 23.3, 24.8, 26.1, 29.1, 31.6, \mathbf{33.4}, 40.3, 42.9, 44.9, 49.5, 56.2, 67.4, 97.5, 203.3, 275.1 \ &\tilde{x}_{\text{orig}} = X_{(10)} = 33.4 \ &\text{Sorted new (18 values): } 10.1, 14.1, 15.6, 15.7, 23.3, 24.8, 26.1, 29.1, \mathbf{31.6, 33.4}, 40.3, 42.9, 44.9, 49.5, 56.2, 67.4, 97.5, 203.3 \ &\tilde{x}_{\text{new}} = \frac{31.6 + 33.4}{2} = 32.5 \ &|\Delta \tilde{x}| = |33.4 - 32.5| = 0.9 \end{aligned} $$ ## Compare the changes $$ \begin{aligned} &|\Delta \mu| = 12.12 \ &|\Delta \tilde{x}| = 0.9 \ &|\Delta \mu| > |\Delta \tilde{x}| \end{aligned} $$

A. The mean was affected more than the median.

B. The median was affected more than the mean.

C. Both the mean and the median were affected equally.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Measures of Central Tendency Interpretation" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate original and new mean values

Calculate original and new median values

Compare the changes

Answer: