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Mrs. Tinney’s class has the following scores on their most recent test:

100 98 95 88 72 66 60 78 80
80


1. Calculate the five-number summary and use it to draw (and label) your box and whisker plot on a number line. Show your work for all calculations.


2. If Mrs. Aguiar’s class has a five-number summary of 50, 60, 70, 80, and 95, which class’ scores are more consistent? How do you know?


3. The mean for Mrs. Tinney’s class is 85 and the mean for Mrs. Aguiar’s class is 70. What conjecture could we make about symmetry? Explain.

1 Answer

3 votes

Answer:

1. Five-number summary for Mrs. Tinney's class scores:Minimum (Min): 60

First Quartile (Q1): 72

Median (Q2 or Median): 80

Third Quartile (Q3): 88

Maximum (Max): 100To draw the box and whisker plot, we can plot these

values on a number line:

| | | | |

60 72 80 88 95 100

We can then draw a box from Q1 to Q3, with a line inside representing the median (Q2), and draw whiskers from the box to Min and Max.

2. Mrs. Aguiar's class scores are more consistent compared to Mrs. Tinney's class scores. This can be determined from the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1) in a box and whisker plot. A smaller IQR indicates less variability in the data and hence more consistency. In this case, Mrs. Aguiar's class has an IQR of 80 - 60 = 20, while Mrs. Tinney's class has an IQR of 88 - 72 = 16. Therefore, Mrs. Aguiar's class scores are more consistent.

3. Based on the mean values, we can make a conjecture about symmetry. The mean is a measure of central tendency that represents the average of a set of data points. If the mean is close to the median, it suggests that the data is approximately symmetric. In this case, the mean for Mrs. Tinney's class is 85, which is closer to the median (Q2) of 80, indicating approximate symmetry. On the other hand, the mean for Mrs. Aguiar's class is 70, which is not close to the median of 80, suggesting that the data may not be symmetric. However, further analysis using other measures of skewness or visualization techniques may be needed for a more conclusive assessment of symmetry.

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