Q 92. - The Practice of Statistics for AP

Question

Acing the first test Here are the scores of Mrs. Liao’s students on their first statistics test:

(a) Make a boxplot of the test score data by hand. Be sure to check for outliers.

(b) How did the students do on Mrs. Liao’s first test? Justify your answer.

Step-by-Step Solution

Answer

Part (b) The students performed very well.

Part (a) The box plot is 

Part (a) Step 1: Given information

The table is 

93	93	87.5	91	94.5	72	96	95	93.5	93.5	73
82	45	88	80	86	85.5	87.5	81	78	86	89
93	91	98	85	82.5	88	94.5	43

Part (a) Step 2: Concept

A boxplot is a frequent data analysis graph.

Part (a) Step 3: Calculation

The following is a box plot of Mrs. Liao's students' test score data on their first statistics test: 

To look for outliers, we'll calculate the IQR and then determine the upper and lower bounds: $$\begin{gathered} IQR =Q_3- {Q }_1= 93.25 - 81.5 = 11.75 \\ IQRx1.5 = 11.75x1.5 = 17.625 \\ {Q }_3+ 60 = 93.25 + 17.625 = 110.875 \\ {Q}_1-60=81.5-17.625 = 63.875 \end{gathered}$$

Any figure between $110.875$ and $63.875$ is considered an anomaly. The outliers in this situation are $43$ and $45$ Thus, the box-plot is made for the given data.

Part (b) Step 1: Calculation

The first statistics test was a success for the vast majority of students. Only two students out of thirty were unable to achieve satisfactory results. Because the median score is $87.75$ and Q1 is also above $70\%$, the majority of students have scored in excess of $70$. Only two students, who received scores of $43$ and $45$, scored in the lower half of the range. Therefore, the students performed very well.