Question

Find the 5 number summary for the data shown36121630424950556467848789905 number summary(from least to greatest):

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Place the numbers from the least to greatest

`3,6,12,16,30,42,49,50,55,64,67,84,87,89,90`

STEP 2: Find the median

The median is the number in the middle position. The middle position will be the 8th and the number there is 50.

Median is 50

STEP 3: Find the lower quartile

The lower quartile is the median of the data set to the left of the median

`\begin{gathered} The\text{ data are:} \\ (3,6,12,16,30,42,49) \\ median=16 \\ Q1=16 \end{gathered}`

16 is the lower quartile

STEP 4: Find the upper quartile

The upper quartile is the median of the data set to the right of the median

`\begin{gathered} (55,64,67,84,87,89,90) \\ median=84 \\ Q3=84 \end{gathered}`

84 is the upper quartile

STEP 5: Find the maximum and minimum of the data

`\begin{gathered} Minimum=3 \\ Maximum=90 \end{gathered}`

STEP 6: Find the Interquartile range

`Q3-Q1=84-16=68`

Hence, the 5-number summary is given as:

Minimum = 3

Lower quartile = 16

Median = 50

Upper quartile = 84

Maximum = 90