Q R1.7. - The Practice of Statistics for AP

Question

Guinea pig survival times Here are the survival times in days of $72$guinea pigs after they were injected with infectious bacteria in a medical experiment.$52$ Survival times, whether of machines under stress or cancer patients after treatment, usually have distributions that are skewed to the right.

(a) Make a histogram of the data and describe its main features. Does it show the expected right-skew?

(b) Now make a boxplot of the data. Be sure to check for outliers. 

Step-by-Step Solution

Answer

Part (a) A histogram will convey a rough sense of the Skewness or shape, but two numerical measures of shape will provide precise data.

Part (b) $(329 380 403 511 522 548)$ are outliner.

Part (a) Step 1: Given information

The table is 

43	45	53	56	56	57	58	66	67	73	74	79
80	80	81	81	81	82	83	83	84	88	89	91
91	92	92	97	99	99	100	100	101	102	102	102
103	104	107	108	109	113	114	118	121	123	126	128
137	138	139	144	145	147	156	162	174	178	179	184
191	198	211	214	243	249	329	380	403	511	522	598

Part (a) Step 2: Concept

A histogram is a graphing tool that is often used. It's used to summarise data that's either discrete or continuous and measured on an interval scale. It's commonly used to demonstrate the key aspects of data distribution in a user-friendly manner.

Part (a) Step 3: Explanation

The graph is 

The histogram is built from the above data, and it is also seen from the above histogram that the given set of data is favorably or right side skewed, implying that the median is the measure of central tendency. A histogram will convey a rough sense of the Skewness or shape, but two numerical measures of shape will provide precise data.

Part (b) Step 1: Calculation

The graph is 

From the above box plot, it is observed that, 

1. The minimum: $43$

2. $Q1: 82.5$

3. The median: $102.5$

4. $Q3: 151.5$ 

5. The maximum: $598$

Outliners: 

$$\begin{gathered} 82.5 - 1.5 \left(69\right) = -21 \\ 151.5 + 1.5 \left(69\right) = 255 \end{gathered}$$

$(329 380 403 511 522 548)$ are outliners.