Question

the table below shows the calories of one serving of vegetables.

find the range, lower quartile, and upper quartile of the data.

range = 57, q_1 = 10, q_3 = 30
range = 45, q_1 = 9, q_3 = 66

Explanation:

Order the dataset

Using the Ordering Numbers knowledge point

$$ 9, 10, 17, 17, 25, 30, 66 $$

Calculate the range

Using the Range of Data knowledge point

$$ \text{Range} = 66 - 9 = 57 $$

Find the lower and upper quartiles

The median of the dataset \(9, 10, 17, 17, 25, 30, 66\) is the middle value:

$$ \text{Median} = 17 $$

The lower half of the data consists of the values below the median:

$$ 9, 10, 17 $$

The lower quartile \(Q_1\) is the median of this lower half:

$$ Q_1 = 10 $$

The upper half of the data consists of the values above the median:

$$ 25, 30, 66 $$

The upper quartile \(Q_3\) is the median of this upper half:

$$ Q_3 = 30 $$

Identify the correct option

The calculated values are:

$$ \text{Range} = 57, \quad Q_1 = 10, \quad Q_3 = 30 $$

This matches the first option.

Answer:

• (A) Range = 57, \(Q_1 = 10\), \(Q_3 = 30\) (Correct answer)
• (B) Range = 45, \(Q_1 = 9\), \(Q_3 = 66\)