Question

a. what quarter has the smallest spread of data?
second
first
third
fourth
b. what is that spread?
i
c. what quarter has the largest spread of data?
first
third
second
fourth
d. what is that spread?
e. find the inter quartile range (iqr):
f. which interval has the most data in it?
30 - 36
36 - 42
42 - 100
26 - 29

Explanation:

Step1: Identify quartile ranges

First - from 24 to 27, spread is \(27 - 24=3\). Second - from 27 to 29, spread is \(29 - 27 = 2\). Third - from 29 to 36, spread is \(36 - 29=7\). Fourth - from 36 to 42, spread is \(42 - 36 = 6\).

Step2: Answer part a

The second quartile has the smallest spread.

Step3: Answer part b

The spread of the second quartile is 2.

Step4: Answer part c

The third quartile has the largest spread.

Step5: Answer part d

The spread of the third quartile is 7.

Step6: Calculate IQR

IQR = Third - First quartile. First quartile value is 27, third quartile value is 36. So \(IQR=36 - 27=9\).

Step7: Answer part f

The box - and - whisker plot shows that the middle 50% of the data (from 27 to 36) has the most data. The interval \(30 - 36\) is part of this middle 50% range.

Answer:

a. Second
b. 2
c. Third
d. 7
e. 9
f. 30 - 36