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 median
range and interquartile range
mean and range

Explanation:

• Range: The range is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value}\). It gives an idea of how much the data values are spread out from the smallest to the largest value in the data set.
• Inter - quartile range (IQR): The IQR is calculated as \(IQR = Q_{3}-Q_{1}\), where \(Q_{1}\) is the first quartile (25th percentile) and \(Q_{3}\) is the third quartile (75th percentile). It represents the spread of the middle 50% of the data.
• Median: The median is the middle - value of a data set when it is ordered. It is a measure of central tendency, not a measure of spread.
• Mean: The mean is calculated as \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). It is also a measure of central tendency, not a measure of spread.

Since we are looking for measures of spread (variability) of the scores, and range and inter - quartile range are measures of spread while mean and median are measures of central tendency.

Answer:

range and interquartile range