Question

jada is studying the variability of her quiz scores. which pair of statistics best describes the spread of scores?

○ median and interquartile range
○ mean and range
○ mean and median
○ range and interquartile range

Explanation:

• Range: It is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value}\). It gives the overall spread of the data from the lowest to the highest score.
• Inter - quartile range (IQR): \(IQR = Q_{3}-Q_{1}\), where \(Q_{1}\) is the first quartile (25th percentile) and \(Q_{3}\) is the third quartile (75th percentile). It measures the spread of the middle 50% of the data, which is less affected by outliers compared to the range.
• Mean: \( \text{Mean}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). It is a measure of central tendency, not a measure of spread.
• Median: It is the middle - value of a sorted data set. It is a measure of central tendency, not a measure of spread.

Since we are looking for measures of spread (variability), and the mean and median are measures of central tendency, we can eliminate the options with mean and median. The range and inter - quartile range are both measures of spread.

Answer:

range and interquartile range