Question

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music festival tickets
the data shown represents the prices of tickets for a music festival.
$12, $35, $43, $81, $46, $30, $41, $95, $103, $43, $96, $76
**question 6 – create a box and whiskers plot for the data given in music festival tickets

Explanation:

Step1: Order the data

First, we need to order the data from least to greatest. The data is: $12, 30, 35, 41, 43, 43, 46, 76, 81, 95, 96, 103$ (Note: There was a typo in the original data, assuming $76$ instead of $70$ as per the plot labels and logical ordering).

Step2: Find the minimum and maximum

The minimum value (smallest number) is $12$, and the maximum value (largest number) is $103$.

Step3: Find the median (Q2)

Since there are 12 data points (even number), the median is the average of the 6th and 7th values. The 6th value is $43$ and the 7th value is $46$. So, the median $Q2=\frac{43 + 46}{2}=\frac{89}{2} = 44.5$.

Step4: Find the lower quartile (Q1)

The lower half of the data is the first 6 values: $12, 30, 35, 41, 43, 43$. The median of this lower half (Q1) is the average of the 3rd and 4th values. The 3rd value is $35$ and the 4th value is $41$. So, $Q1=\frac{35+41}{2}=\frac{76}{2}=38$.

Step5: Find the upper quartile (Q3)

The upper half of the data is the last 6 values: $46, 76, 81, 95, 96, 103$. The median of this upper half (Q3) is the average of the 3rd and 4th values. The 3rd value is $81$ and the 4th value is $95$. So, $Q3=\frac{81 + 95}{2}=\frac{176}{2}=88$.

Step6: Draw the Box - and - Whisker Plot

• The whiskers extend from the minimum ($12$) to the maximum ($103$).
• The box is drawn from Q1 ($38$) to Q3 ($88$), and a line is drawn inside the box at the median ($44.5$).

To create the box - and - whisker plot:

1. Draw a number line that includes the range of the data (from $12$ to $103$).
2. Plot the minimum value ($12$) and the maximum value ($103$) as the endpoints of the whiskers.
3. Draw a box with the left - hand side at Q1 ($38$) and the right - hand side at Q3 ($88$).
4. Draw a vertical line inside the box at the median ($44.5$).

Answer:

The box - and - whisker plot has: minimum = $12$, Q1 = $38$, median = $44.5$, Q3 = $88$, maximum = $103$. The plot is constructed with whiskers from $12$ to $103$, a box from $38$ to $88$, and a line at $44.5$ inside the box.