Question

22 given the following data set: 65, 70, 70, 70, 70, 80, 80, 80, 85, 90, 90, 95, 95, 95, 100 which representations are correct for this data set? (1) i and ii, only (2) i and iii, only (3) ii and iii, only (4) i, ii, and iii

Explanation:

Step1: Analyze dot - plot (I)

The dot - plot correctly represents the frequency of each data value in the set. For example, there is 1 dot at 65, 4 dots at 70, etc., which matches the given data set.

Step2: Analyze box - plot (II)

To create a box - plot, we first find the five - number summary: minimum = 65, Q1 (first quartile). There are 15 data points. The position of Q1 is $\frac{15 + 1}{4}=4$th value, so Q1 = 70. The median (Q2) is the 8th value, so Q2 = 80. Q3 is at $\frac{3(15 + 1)}{4}=12$th value, so Q3 = 95, and maximum = 100. The box - plot is drawn correctly based on these values.

Step3: Analyze histogram (III)

The histogram has intervals: 61 - 71, 71 - 81, 81 - 91, 91 - 101. The frequencies for these intervals calculated from the data set match the heights of the bars in the histogram. For the interval 61 - 71, there are 5 values (65, 70, 70, 70, 70), for 71 - 81 there are 3 values (80, 80, 80), for 81 - 91 there are 2 values (85, 90), and for 91 - 101 there are 5 values (90, 95, 95, 95, 100).

Answer:

(4) I, II, and III