Question

1. (review from unit 1) 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? state and defend your answer/explain your reasoning.

Explanation:

Step1: Organize data

The data set is 65, 70, 70, 70, 70, 80, 80, 80, 85, 90, 90, 95, 95, 95, 100.

Step2: Find minimum and maximum

The minimum value is 65 and the maximum value is 100.

Step3: Calculate quartiles

First, find the median (Q2). Since there are 15 data - points, the median is the 8th value, so Q2 = 80.
The lower half of the data is 65, 70, 70, 70, 70, 80, 80. The median of the lower half (Q1) is 70.
The upper half of the data is 85, 90, 90, 95, 95, 95, 100. The median of the upper half (Q3) is 95.

Step4: Analyze box - and - whisker plot (II)

The box - and - whisker plot has the minimum at 65, Q1 at 70, Q2 at 80, Q3 at 95 and maximum at 100, which is consistent with our calculations.
The dot - plot (I) correctly shows the frequency of each data value.
The histogram (III) can also represent the data by grouping the data into intervals.

Answer:

I, II, and III are correct for this data set.