the accompanying table shows trade deficits for a certain country (in billions of dollars) to 19 other countries for a recent year. complete parts (a) through (c) below.

(a) find the mean and median of the trade deficits.
the mean of the trade deficits is \$57.94 billion.
(round to two decimal places as needed.)
the median of the trade deficits is \$33.4 billion.
(type an integer or a decimal. do not round.)

(b) find the mean and the median of the trade deficits without trade deficit to country a. which measure of central tendency, the mean or the median, was affected more by the elimination of trade deficits to country a?
the mean of the trade deficits is \$45.88 billion.
(round to two decimal places as needed.)
the median of the trade deficits is \$32.5 billion.
(type an integer or a decimal. do not round.)

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.

(c) the trade deficits for this country to country z were \$19.8 billion. find the mean and the median with the trade deficits to country z added to the original data set. which measure of central tendency was affected more by adding trade deficits to country z?
the mean of the trade deficits is \$ billion.
(round to two decimal places as needed.)

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

Question

the accompanying table shows trade deficits for a certain country (in billions of dollars) to 19 other countries for a recent year. complete parts (a) through (c) below.

(a) find the mean and median of the trade deficits.
the mean of the trade deficits is \$57.94 billion.
(round to two decimal places as needed.)
the median of the trade deficits is \$33.4 billion.
(type an integer or a decimal. do not round.)

(b) find the mean and the median of the trade deficits without trade deficit to country a. which measure of central tendency, the mean or the median, was affected more by the elimination of trade deficits to country a?
the mean of the trade deficits is \$45.88 billion.
(round to two decimal places as needed.)
the median of the trade deficits is \$32.5 billion.
(type an integer or a decimal. do not round.)

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.

(c) the trade deficits for this country to country z were \$19.8 billion. find the mean and the median with the trade deficits to country z added to the original data set. which measure of central tendency was affected more by adding trade deficits to country z?
the mean of the trade deficits is \$   billion.
(round to two decimal places as needed.)

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

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "blank_filling_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 the new mean with Country Z added $$ \begin{aligned} &\text{Original sum of } 19 \text{ values} = 19 \times 57.9421 \approx 1100.9\ &\text{Sum from table} = 275.1 + 203.3 + 49.5 + 24.8 + 44.9 + 97.5 + 29.1 + 15.7 + 23.3 + 29.1 + 11.2 + 67.4 + 42.9 + 33.4 + 26.1 + 40.3 + 31.6 + 15.6 + 10.1 = 1100.9\ &\text{New sum with Country Z } (19.8) = 1100.9 + 19.8 = 1120.7\ &\text{New count } (n) = 20\ &\text{New mean} = \frac{1120.7}{20} = 56.035 \approx 56.04 \end{aligned} $$ ## Calculate the new median with Country Z added $$ \begin{aligned} &\text{Sorted original 19 values:} \ &10.1, 11.2, 15.6, 15.7, 23.3, 24.8, 26.1, 29.1, 29.1, 31.6, 33.4, 40.3, 42.9, 44.9, 49.5, 67.4, 97.5, 203.3, 275.1 \ &\text{Insert } 19.8 \text{ into sorted list:} \ &10.1, 11.2, 15.6, 15.7, 19.8, 23.3, 24.8, 26.1, 29.1, \mathbf{29.1}, \mathbf{31.6}, 33.4, 40.3, 42.9, 44.9, 49.5, 67.4, 97.5, 203.3, 275.1 \ &\text{New median (average of 10th and 11th values)} = \frac{29.1 + 31.6}{2} = 30.35 \end{aligned} $$ ## Compare the absolute changes in mean and median $$ \begin{aligned} &\Delta \text{mean} = |57.94 - 56.04| = 1.90\ &\Delta \text{median} = |33.4 - 30.35| = 3.05\ &3.05 > 1.90 \implies \text{The median was affected more.} \end{aligned} $$ ## Question 1 The mean of the trade deficits is $56.04 billion. ## Question 2 The median of the trade deficits is $30.35 billion. ## Question 3 Which measure of central tendency was affected more by adding trade deficits to Country Z? 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": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Measures of Central Tendency" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the new mean with Country Z added

Calculate the new median with Country Z added

Compare the absolute changes in mean and median

Answer:

Question 1

Question 2

Question 3