Question

Find the 5 data points needed for a box plot of the given data set: { 8, 19, 11, 20, 2, 14, 17, 9, 15}

Give the answers in order from least to greatest.

Data Point 1:

Data Point 2:

Data Point 3:

Data Point 4:

Data Point 5:

Answer 1

Answers:

• Data Point 1: 2
• Data Point 2: 8.5
• Data Point 3: 14
• Data Point 4: 18
• Data Point 5: 20

The boxplot is shown below.

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Step-by-step explanation:

What your teacher wants is the five number summary.

This consists of:

1. Min
2. Q1
3. Median
4. Q3
5. Max

Given in that exact order.

The given data set is { 8, 19, 11, 20, 2, 14, 17, 9, 15}

This sorts to {2, 8, 9, 11, 14, 15, 17, 19, 20}

From this sorted set, we see that 2 is the smallest item. So this is the min value. This is data point 1.

The max is the largest item, which in this case is 20, so this value goes in the box for data point 5.

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Count out the number of values in the sorted set. You should count out n = 9 items.

Because n is odd, this means the median is in slot n/2 = 9/2 = 4.5 = 5

The value in the 5th slot is 14 which is the median (data point 3).

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Once you determine the median, break the sorted set up like so

L = {2, 8, 9, 11}

U = {15, 17, 19, 20}

L is the lower set of values smaller than the median

U is the upper set of values larger than the median

The median itself is not part of set L and not part of set U either. It's ignored entirely from this point on.

From here, we find the middle values of L and U

You should find that the middle value of L is (8+9)/2 = 17/2 = 8.5 which is the value of Q1 (data point 2)

And also, the middle value of set U is (17+19)/2 = 36/2 = 18 which is the value of Q3 (data point 4)

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To wrap everything up, we have this five number summary

1. Min = 2
2. Q1 = 8.5
3. Median = 14
4. Q3 = 18
5. Max = 20

These will determine the features of the boxplot as shown below.

In this case, there are no outliers.