Question

10 different ways to represent data are shown below. which data representations have a median of 2? (1) i and ii, only (2) i and iii, only (3) ii and iii, only (4) i, ii, and iii

Explanation:

Step1: Find median of I

Count the number of data - points in the dot - plot (I). There are 15 data - points. The median is the 8th ordered data - point. Counting from the left, the 8th data - point is 2.

Step2: Find median of II

In a box - and - whisker plot (II), the line inside the box represents the median. Here, the line inside the box is at 2, so the median is 2.

Step3: Find median of III

For the histogram (III), we first find the cumulative frequencies. The total number of data - points is \(1 + 3+5 + 3+4+3+2=21\). The median is the 11th ordered data - point. Cumulative frequencies: 1 (for 0), \(1 + 3=4\) (for 1), \(4 + 5 = 9\) (for 2), \(9+3 = 12\) (for 3). The 11th data - point falls in the class with value 2, so the median is 2.

Answer:

(4) I, II, and III