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Example1

Title: Box Plots & Outlier Identification

Grade Lesson s6-l6

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2

A group of friends recorded the prices (in dollars) they paid for concert tickets. Make a box-and-whisker plot that represents the data. Describe the distribution: 75, 60, 80, 90, 65, 70, 85, 95, 70, and 100.

Step: 1

60, 65, 70, 70, 75, 80, 85, 90, 95, and 100
Minimum = 60
Maximum = 100

The median of the lower half of the data.
Q1 = Median of {60, 65, 70, 70, and 75} = 70

The median of the entire data set.
Q2 = Median of {60, 65, 70, 70, 75, 80, 85, 90, 95, and 100} = 77.5

The median of the upper half of the data.
Q3 = Median of {80, 85, 90, 95, and 100} = 90.

Explanation:

Here, we define the smallest number as the minimum and the largest number as the maximum. Then, we calculate the median values for the lower half, upper half, and the entire dataset.

Step: 2

The box-and-whisker plot of concert ticket prices shows the following characteristics:

Minimum Value: The lowest price is $60.
First Quartile (Q1): 25% of the prices are below $70.
Median (Q2): The median price is $77.5, indicating that 50% of the prices are below this value.
Third Quartile (Q3): 75% of the prices are below $90.
Maximum Value: The highest price is $100.

Explanation:

Here, we write all the values.

Step: 3

The interquartile range (IQR) is the difference between Q3 and Q1, which is 90 − 70 = 20.
This indicates that the middle 50% of the data span a range of $20.

The data appears to be roughly symmetric, as the median is centered between the
first and third quartiles, and the whiskers extend relatively equally on both sides.

Most of the concert ticket prices cluster around the median ($77.5), with the range
extending from $60 to $100 without any extreme outliers.

Overall, the distribution shows that concert ticket prices in this dataset tend to cluster around $77.5, with a fairly symmetric distribution from $60 to $100.

Explanation:

Therefore, the given set is a Symmetric distribution.