Question

box-and-whisker plot
make box-and-whisker plots for the given data.

1. handwritten data, then

minimum: ____
maximum: ____
q₁: ____
q₂: ____
q₃: ____
number line with 0, 8, 9, 10, 11, 14, 17, 20, 23, 29, 30, 31, 40

1. 58, 67, 44, 72, 51, 42, 50, 46, 69

minimum: ____
maximum: ____
q₁: ____
q₂: ____
q₃: ____
number line from 40 to 85

1. 67, 100, 94, 77, 90, 62, 79, 68, 95, 86, 73, 84

minimum: ____
maximum: ____
q₁: ____
q₂: ____
q₃: ____
number line from 60 to 100

Explanation:

Problem 2: Data set: 58, 67, 44, 72, 51, 42, 50, 46, 69

Step 1: Order the data

First, we order the data from smallest to largest: \( 42, 44, 46, 50, 51, 58, 67, 69, 72 \)

Step 2: Find Minimum and Maximum

The minimum value is the smallest number, and the maximum value is the largest number.
Minimum: \( 42 \)
Maximum: \( 72 \)

Step 3: Find the Median ( \( Q_2 \))

The median is the middle value of the ordered data. Since there are 9 data points (odd number), the median is the 5th value.
Median ( \( Q_2 \)): \( 51 \)

Step 4: Find \( Q_1 \) (Median of the lower half)

The lower half of the data is \( 42, 44, 46, 50 \) (the values before the median). Since there are 4 data points (even number), the median of the lower half is the average of the 2nd and 3rd values.
\( Q_1=\frac{44 + 46}{2}=\frac{90}{2} = 45 \)

Step 5: Find \( Q_3 \) (Median of the upper half)

The upper half of the data is \( 58, 67, 69, 72 \) (the values after the median). Since there are 4 data points (even number), the median of the upper half is the average of the 2nd and 3rd values.
\( Q_3=\frac{67+69}{2}=\frac{136}{2}=68 \)

Step 1: Order the data

First, we order the data from smallest to largest: \( 62, 67, 68, 73, 77, 79, 84, 86, 90, 94, 95, 100 \)

Step 2: Find Minimum and Maximum

The minimum value is the smallest number, and the maximum value is the largest number.
Minimum: \( 62 \)
Maximum: \( 100 \)

Step 3: Find the Median ( \( Q_2 \))

The median is the average of the two middle values since there are 12 data points (even number). The two middle values are the 6th and 7th values.
Median ( \( Q_2 \)): \( \frac{79 + 84}{2}=\frac{163}{2}=81.5 \)

Step 4: Find \( Q_1 \) (Median of the lower half)

The lower half of the data is \( 62, 67, 68, 73, 77, 79 \) (the first 6 values). The median of the lower half is the average of the 3rd and 4th values.
\( Q_1=\frac{68 + 73}{2}=\frac{141}{2}=70.5 \)

Step 5: Find \( Q_3 \) (Median of the upper half)

The upper half of the data is \( 84, 86, 90, 94, 95, 100 \) (the last 6 values). The median of the upper half is the average of the 3rd and 4th values.
\( Q_3=\frac{90+94}{2}=\frac{184}{2} = 92 \)

Answer:

Minimum: \( 42 \)
Maximum: \( 72 \)
\( Q_1: 45 \)
\( Q_2: 51 \)
\( Q_3: 68 \)

Problem 3: Data set: 67, 100, 94, 77, 90, 62, 79, 68, 95, 86, 73, 84