Question

the bar graphs below show the percentage of students who received each score on their last english paper and math test. determine whether each graph has a larger or smaller standard deviation.

Explanation:

Step1: Recall standard deviation concept

Standard deviation measures data spread. More spread out data has larger standard deviation; clustered data has smaller.

Step2: Analyze Math Score graph

Math scores: 60 (35%), 70 (20%), 80 (5%), 90 (40%). Scores are at 60, 70, 80, 90 with 80 having low percentage. Data is spread between 60 - 90, with two peaks (60, 90) and a low at 80.

Step3: Analyze English Score graph

English scores: 60 (10%), 70 (35%), 80 (50%), 90 (5%). Scores cluster around 70 - 80 (high percentages at 70, 80), with lower at 60, 90. Data is more clustered.

Step4: Compare standard deviations

Math data is more spread out (peaks at 60, 90; low at 80). English data is clustered at 70 - 80. So Math graph has larger standard deviation, English has smaller.

Answer:

Math Score graph: Larger
English Score graph: Smaller