find the mean, median, and mode of each data set. if no numbers appear more than once in a data set, you can write that there is no mode.

1) $5, 8, 12, 6, 7, 10, 14, 6, 13$
mean = ______
median = ______
mode = ______

2) $12, 16, 9, 17, 13, 8, 16$
mean = ______
median = ______
mode = ______

3) $41, 27, 30, 32, 30, 26, 17, 28, 30$
mean = ______
median = ______
mode = ______

4) $64, 91, 68, 79, 91, 123$
mean = ______
median = ______
mode = ______

5) $81, 72, 70, 80, 77, 77, 60, 67$
mean = ______
median = ______
mode = ______

6) $95, 97, 100, 86, 78, 96$
mean = ______
median = ______
mode = ______

Question

find the mean, median, and mode of each data set. if no numbers appear more than once in a data set, you can write that there is no mode.

1) $5, 8, 12, 6, 7, 10, 14, 6, 13$
mean = ______
median = ______
mode = ______

2) $12, 16, 9, 17, 13, 8, 16$
mean = ______
median = ______
mode = ______

3) $41, 27, 30, 32, 30, 26, 17, 28, 30$
mean = ______
median = ______
mode = ______

4) $64, 91, 68, 79, 91, 123$
mean = ______
median = ______
mode = ______

5) $81, 72, 70, 80, 77, 77, 60, 67$
mean = ______
median = ______
mode = ______

6) $95, 97, 100, 86, 78, 96$
mean = ______
median = ______
mode = ______

Accepted Answer

{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Mean Average" ], "new_concepts": [ "Median", "Mode" ], "current_concepts": [ "Mean Average", "Median", "Mode" ] } ## Calculate statistics for the first dataset $$ \begin{aligned} &\text{Dataset 1: } 5, 8, 12, 6, 7, 10, 14, 6, 13 \quad (n = 9)\ &\text{Sorted: } 5, 6, 6, 7, 8, 10, 12, 13, 14\ &\text{Sum} = 5 + 6 + 6 + 7 + 8 + 10 + 12 + 13 + 14 = 81\ &\text{Mean} = \frac{81}{9} = 9\ &\text{Median} = 8 \quad (\text{5th value})\ &\text{Mode} = 6 \quad (\text{appears twice}) \end{aligned} $$ ## Calculate statistics for the second dataset $$ \begin{aligned} &\text{Dataset 2: } 12, 16, 9, 17, 13, 8, 16 \quad (n = 7)\ &\text{Sorted: } 8, 9, 12, 13, 16, 16, 17\ &\text{Sum} = 8 + 9 + 12 + 13 + 16 + 16 + 17 = 91\ &\text{Mean} = \frac{91}{7} = 13\ &\text{Median} = 13 \quad (\text{4th value})\ &\text{Mode} = 16 \quad (\text{appears twice}) \end{aligned} $$ ## Calculate statistics for the remaining datasets $$ \begin{aligned} &\text{Dataset 3: } 41, 27, 30, 32, 30, 26, 17, 28, 30 \quad (n = 9)\ &\text{Sorted: } 17, 26, 27, 28, 30, 30, 30, 32, 41\ &\text{Sum} = 261 \implies \text{Mean} = \frac{261}{9} = 29\ &\text{Median} = 30, \quad \text{Mode} = 30\ \ &\text{Dataset 4: } 64, 91, 68, 79, 91, 123 \quad (n = 6)\ &\text{Sorted: } 64, 68, 79, 91, 91, 123\ &\text{Sum} = 516 \implies \text{Mean} = \frac{516}{6} = 86\ &\text{Median} = \frac{79 + 91}{2} = 85, \quad \text{Mode} = 91\ \ &\text{Dataset 5: } 81, 72, 70, 80, 77, 77, 60, 67 \quad (n = 8)\ &\text{Sorted: } 60, 67, 70, 72, 77, 77, 80, 81\ &\text{Sum} = 584 \implies \text{Mean} = \frac{584}{8} = 73\ &\text{Median} = \frac{72 + 77}{2} = 74.5, \quad \text{Mode} = 77\ \ &\text{Dataset 6: } 95, 97, 100, 86, 78, 96 \quad (n = 6)\ &\text{Sorted: } 78, 86, 95, 96, 97, 100\ &\text{Sum} = 552 \implies \text{Mean} = \frac{552}{6} = 92\ &\text{Median} = \frac{95 + 96}{2} = 95.5, \quad \text{Mode} = \text{no mode} \end{aligned} $$ | No. | Dataset | Answer | |---|---|---| | 1 | $5, 8, 12, 6, 7, 10, 14, 6, 13$ | Mean = 9, Median = 8, Mode = 6 | | 2 | $12, 16, 9, 17, 13, 8, 16$ | Mean = 13, Median = 13, Mode = 16 | | 3 | $41, 27, 30, 32, 30, 26, 17, 28, 30$ | Mean = 29, Median = 30, Mode = 30 | | 4 | $64, 91, 68, 79, 91, 123$ | Mean = 86, Median = 85, Mode = 91 | | 5 | $81, 72, 70, 80, 77, 77, 60, 67$ | Mean = 73, Median = 74.5, Mode = 77 | | 6 | $95, 97, 100, 86, 78, 96$ | Mean = 92, Median = 95.5, Mode = no mode | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Statistics", "Mean Average" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate statistics for the first dataset

Calculate statistics for the second dataset

Calculate statistics for the remaining datasets

Answer:

No.	Dataset	Answer
2	\(12, 16, 9, 17, 13, 8, 16\)	Mean = 13, Median = 13, Mode = 16
3	\(41, 27, 30, 32, 30, 26, 17, 28, 30\)	Mean = 29, Median = 30, Mode = 30
4	\(64, 91, 68, 79, 91, 123\)	Mean = 86, Median = 85, Mode = 91
5	\(81, 72, 70, 80, 77, 77, 60, 67\)	Mean = 73, Median = 74.5, Mode = 77
6	\(95, 97, 100, 86, 78, 96\)	Mean = 92, Median = 95.5, Mode = no mode