Question

The survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment is displayed in the table.

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

To access the complete data set, click the link for your preferred software format:

Excel  Minitab  JMP  SPSS TI  R  Mac-TXT   PC-TXT  CSV CrunchIt!

(a) Use the software of your choice to graph the distribution and describe its main features. Select the best description from the given choices.

The distribution is strongly left‑skewed, with the center around 100 days and a range from about 0 days to about 600 days.

The distribution is strongly right‑skewed, with the center around 100 days and a range from about 0 days to about 600 days.

The distribution is bimodal, with the center around 100 days and a range from about 0 days to about 600 days.

The distribution is Normal, with the center around 300 days and a range from about 0 days to about 600 days.

(b) Use the software of your choice to calculate the five‑number summary for these data. (Enter your answers rounded to one decimal place.)

Min=

days

?1=

days

Median=

days

?3=

days

Max=

days

Calculate the mean for these data. (Enter your answer rounded to one decimal place.)

mean=

days

Summarize your findings. Choose the best statement.

The median is closer to ?1 than to ?3

The mean and the median are almost equal.

The median is closer to ?3 than to ?1

The mean is closer to ?1 than to ?3

Answer 1

We will use excel to do the analysis

a) We can see that the minimum value is 43 and the maximum of 598. We will create 12 classes of width 50 each starting from 0-50 to ending at 550-600

We create the following bin ranges in excel

Next we create a histogram using data-->data analysis-->histogram

get the following histogram

format as needed

We can see the following

The longest bar is at 100, hence the distribution is centered 100 days. There is only one peak, that means this is unimodal. The rigth tail is longer than the left tail, indicating that the distribution is skewed towards right.

Hence the following description is appropriate

The distribution is strongly right‑skewed, with the center around 100 days and a range from about 0 days to about 600 days.

b)  the five‑number summary

We calculate the 5 number summary using the function quartile.inc()

get the following

Calculate the mean for these data using

mean is

days

We will check each of these statements

• The median is closer to ?1 than to ?3:
  • Median -Q1=102.5-82.8 = 19.8
  • Q3-Median = 149.3-102.5 = 46.8
  • Since the difference between median and Q1 is less than Q3 and median, median is closer to Q1 than Q3
  • the statement is TRUE
• The mean and the median are almost equal.
  • mean is 141.8 and the median is 102.5, they are not equal.
  • the statement is FALSE
• The median is closer to ?3 than to ?1
  • Since the First statement is true, this can not be true
  • This statement is FALSE
• The mean is closer to ?1 than to ?3
  • Mean - Q1 = 141.8-82.8 = 59.1 and Q3- mean= 149.3-141.8=7.4
  • Mean is not closer to Q1 than to Q3
  • The statement is FALSE

The best statement is The median is closer to ?1 than to ?3