Question

According to U.S. climate data, the monthly average high temperatures, in degrees Fahrenheit, for the city of Chicago are listed below. 32, 34, 43, 55, 65, 75, 81, 79, 73, 61,47, 36 Find the five-number summary for this data. Select the correct answer below (A) Sample minimum: 32, Sample maximum: 36 Q1:49, Median: 78, Q3:67 (B) Sample minimum: 32, Sample maximum: 81 Q1:43, Median: 58, Q3: 73 (C) Sample minimum: 32, Sample maximum: 81 Q1:39.5, Median: 58, Q3: 74 (D) Sample minimum: 32, Sample maximum: 8 Q1:39.5, Median: 61, Q3:74

Answer 1

Answer: (C) Sample minimum: 32, Sample maximum: 81 Q1:39.5, Median: 58, Q3: 74

Step-by-step explanation:

Five number summary for a data contains :

Minimum value

First quartile $(Q_1)$

Median

Third quartile $(Q_3)$

Maximum value.

Given data : 32, 34, 43, 55, 65, 75, 81, 79, 73, 61,47, 36

Arrange in order →32, 34, 36, 43,47, 55, 61, 65, 73, 75, 79, 81

Total values = 12 (even)

⇒ Median = Mean of the middle most two values.

$=\dfrac{55+61}{2} =58$

First quartile = Median of first half (32, 34, 36, 43,47, 55)

$Q_1=\dfrac{36+43}{2}=39.5$

Third quartile = Median of first half (61, 65, 73, 75, 79, 81)

$Q_3=\dfrac{73+75}{2}=74$

Also, Sample Minimum value = 32

Sample Maximum value=81

Therefore , the five-number summary for this data :

Sample Minimum=32

Sample Maximum=81

Median = 58

$Q_1=39.5$

$Q_3=74$

Hence, the correct option is (C) Sample minimum: 32, Sample maximum: 81 Q1:39.5, Median: 58, Q3: 74