Question

the prices of a cup of coffee at 9 different coffee shops are listed below.
select the five - number summary that represents the data.
coffee pri
$1.44 $1.30
$1.52 $1.75
$1.61 $1.68
minimum $1.45
first quartile $1.62
median $1.75
third quartile $1.61
maximum $1.38
minimum $1.25
first quartile $1.34
median $1.52
third quartile $1.65
maximum $1.75
minimum $1.25
first quartile $1.38
median $1.52
third quartile $1.62
maximum $1.75
minimum $1.25
first quartile $1.34
median $1.48
third quartile $1.65
maximum $1.75

Explanation:

Step1: Sort the data

First, we need to sort the data in ascending order. The data is: \(\$1.44,\$1.30,\$1.52,\$1.75,\$1.61,\$1.68\). After sorting, it becomes \(\$1.25,\$1.30,\$1.38,\$1.44,\$1.52,\$1.61,\$1.68,\$1.75\) (assuming there was a typo in the original data entry and the correct sorted set includes \(1.25\) and \(1.38\) which are in the options).

Step2: Find the minimum

The minimum value is the first value in the sorted data set. So, \(\text{Minimum}=\$1.25\).

Step3: Find the first quartile (\(Q_1\))

The first quartile is the median of the lower half of the data. The lower half of the data \(\$1.25,\$1.30,\$1.38,\$1.44\). The median of this set (for \(n = 4\) data points, the median is the average of the 2nd and 3rd values). \(\frac{1.30 + 1.38}{2}=\$1.34\).

Step4: Find the median

The median is the middle value of the sorted data set. For \(n=8\) data points, the median is the average of the 4th and 5th values. \(\frac{1.44+1.52}{2}=\$1.48\) (wait no, for \(n = 8\), the formula for the median position is \(\frac{n + 1}{2}=4.5\), but actually for \(n=8\), median is \(\frac{x_4+x_5}{2}\). Wait no, original data count: if we assume the full data set (since 5 - number summary is for a set, and from options we can infer). Wait actually, if we have 8 data points (after proper sorting with all values), the median is \(\frac{1.44 + 1.52}{2}=1.48\) (but wait no, if we consider the correct sorted data as \(1.25,1.30,1.38,1.44,1.52,1.61,1.68,1.75\) (8 values). The median is \(\frac{1.44+1.52}{2} = 1.48\). The first quartile: lower half \(1.25,1.30,1.38,1.44\), \(Q_1=\frac{1.30 + 1.38}{2}=1.34\). Third quartile: upper half \(1.61,1.68,1.75\) (wait no, for \(n = 8\), upper half is \(1.61,1.68,1.75\) (no, for \(n=8\), upper half is from \(x_5\) to \(x_8\): \(1.52,1.61,1.68,1.75\). \(Q_3=\frac{1.61+1.68}{2}=1.645\approx1.65\). Maximum is \(1.75\).

Answer:

Minimum: \(\$1.25\), First Quartile: \(\$1.34\), Median: \(\$1.48\), Third Quartile: \(\$1.65\), Maximum: \(\$1.75\) (corresponding to the option where these values are present)