Question

Suppose a set of data was arranged in order from lowest to highest values as shown below, where each letter or symbol had an unknown numerical value:

b, a, #, v, w, y, @, p, c, m, n, x, q, &, k, +, r, $

1. (a) Find the five number summary.

Answer 1

Number of data = 18

>> Minimum value = b

>> Maximum value = $

>> Median = The median is the value separating the higher half from the lower half of a data sample. Here, the two middlemost values are c and m. Hence, median is (c+m)/2

>> The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set. Here, first quartile is the middle value of first 9 numbers. Hence, first quartile is w.

>> The third quartile (Q3) is the middle value between the median and the highest value of the data set. Here, third quartile is the middle value of last 9 numbers. Hence, third quartile is &.

(a) The five number summary:

{Minimum, First quartile, Median, Third quartile, Maximum}

= {b, w, (c+m)/2, &, $}