Question

The following frequency table summarizes a set of data. What is the five-number summary?

Answer 1

We are given a frequency table.

Let us find the 5-number summary of the data.

Recall that the 5-number summary is given by

Minimum, Quarter 1, Median, Quarter 3, Maximum

From the table, we see that

Minimum = 3

Maximum = 12

Now let us create a frequency column

The frequency column tells us that there are a total of 15 data values.

Since 15 is an odd number, the median value will be at

`median=(n+1)/(2)=(15+1)/(2)=(16)/(2)=8th\: \text{place}`

So the median will be at the 8th place, and from the table, we see that the 8th value corresponds to number 8

Therefore, the median is 8

The 1st quarter will be located at

`1st\: quarter=(n+1)/(4)=(15+1)/(4)=(16)/(4)=4th\: \text{place}`

So the 1st quater will be at the 4th place, and from the table, we see that the 4th value corresponds to number 6

Therefore, the 1st quarter is 6

The 3rd quarter will be located at

`\begin{gathered} 3rd\: quarter=median+1st\: quarter \\ 3rd\: quarter=8th\: place+4th\: place \\ 3rd\: quarter=12th\: place \end{gathered}`

So the 3rd quater will be at the 12th place, and from the table, we see that the 12th value corresponds to number 10

Therefore, the 3rd quarter is 10

The five-number summary is

Min = 3, Q1 = 6, Median = 8, Q3 = 10, Max = 12

The 2nd option is the correct answer.