Twenty girls (ages 9-10) competed in the 50-meter freestyle event at a local swim meet. The mean time was 43.70 seconds with a standard deviation of 8.07 seconds. The median time was 40.15 with an IQR of 4.98 seconds. Without looking at a graphical display, what shape would you expect the distribution of swim times to have?

Question

Mathematics

Xavier Sullivan

31 March, 09:12

Twenty girls (ages 9-10) competed in the 50-meter freestyle event at a local swim meet. The mean time was 43.70 seconds with a standard deviation of 8.07 seconds. The median time was 40.15 with an IQR of 4.98 seconds. Without looking at a graphical display, what shape would you expect the distribution of swim times to have?

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Answers (1)

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Jayden Rodriguez · Answer 1

Right or positively skewed

Step-by-step explanation:

From the median and the interquartile range we can find the first and third quartile values Q3=40.15 + (4.98/2) = 42.64 and Q1=37.66.

Now we have enough evidence to conclude that is Right or positively skewed

1. The mean is above the median

2. The mean is 43.70, which is above the third quartile (42.64), meaning that after the mean there's less than 30% of the data.

The evidence suggests that most of the data is concentrated at the bottom of the distribution making it right or positively skewed.