Question

what is the five - number summary for this set of test scores?
90, 95, 89, 84, 74, 99, 97, 86, 93
(2 points)
the minimum is
the value for q1 is
the median of the dataset is
the value for q3 is
the maximum of the dataset is

Explanation:

Step1: Sort the data

First, sort the data set \(74,84,86,89,90,93,95,97,99\) in ascending order (already sorted).

Step2: Find the minimum

The minimum value is the first element of the sorted data set.
\(74\)

Step3: Find Q1 (first quartile)

For \(n = 9\) data points, \(Q1\) is the \(\frac{n + 1}{4}\)th value. \(\frac{9+1}{4}=2.5\)th value. Interpolate between the 2nd and 3rd values. \(Q1=84+(86 - 84)\times0.5=85\)

Step4: Find the median

The median is the \(\frac{n + 1}{2}\)th value. \(\frac{9+1}{2}=5\)th value. Median \(=90\)

Step5: Find Q3 (third quartile)

\(Q3\) is the \(\frac{3(n + 1)}{4}\)th value. \(\frac{3\times(9 + 1)}{4}=7.5\)th value. Interpolate between the 7th and 8th values. \(Q3=95+(97 - 95)\times0.5=96\)

Step6: Find the maximum

The maximum value is the last element of the sorted data set. \(99\)

Answer:

Minimum: \(74\), Q1: \(85\), Median: \(90\), Q3: \(96\), Maximum: \(99\)