Question

haley is helping her brother, brandon, practice his multiplication and division facts. she sets a timer for two minutes and sees how many problems brandon can answer correctly before the timer goes off. the table shows his results. which is the best explanation for why the standard deviation of brandons division scores is greater than that of his multiplication scores? brandons multiplication scores are generally higher than his division scores. the range of brandons multiplication scores is greater than the range of his division scores. the median of brandons division scores is greater than the median of his multiplication scores. brandon has one very low division score. two of brandons division scores are the same. the mean of brandons division scores is less than the mean of his multiplication scores.

Explanation:

Standard deviation measures the spread of data. A very low score (36 in division) increases the spread. Let's check each option:

• "Brandon's multiplication scores are generally higher than his division scores": Standard deviation is about spread, not level of scores.
• "The range of Brandon’s multiplication scores is greater than the range of his division scores": Multiplication range: \(54 - 46=8\). Division range: \(50 - 36 = 14\). So this is false.
• "The median of Brandon’s division scores is greater than the median of his multiplication scores": Multiplication scores in order: \(46,48,51,51,53,54\). Median \(\frac{51 + 51}{2}=51\). Division scores in order: \(36,45,46,46,47,50\). Median \(\frac{46+46}{2} = 46\). So this is false.
• "Brandon has one very low division score": A low - value (36) increases the spread (standard deviation) as it is far from the mean.
• "Two of Brandon’s division scores are the same": Having same scores (like in both multiplication and division) doesn't directly explain higher standard deviation.
• "The mean of Brandon’s division scores is less than the mean of his multiplication scores": Mean of multiplication: \(\frac{48 + 46+51+53+54+51}{6}=\frac{303}{6} = 50.5\). Mean of division: \(\frac{36+46+45+47+50+46}{6}=\frac{270}{6}=45\). But mean difference doesn't explain standard - deviation difference.

Answer:

Brandon has one very low division score.