Question

1. how many values are in the data set whose histogram is shown below? a) 6 b) 22 c) 76 d) 72
2. given the following frequency distribution, how many pieces of data were less than 28.5? class boundaries frequencies 13.5 - 18.5 4 18.5 - 23.5 9 23.5 - 28.5 12 28.5 - 33.5 15 33.5 - 38.5 17 a) 12 b) 13 c) 25 d) 44
3. which graph should be used to represent the frequencies with which certain courses are taken at highlands middle school? a) pareto chart b) time series graph c) pie graph d) pictograph
4. an automobile dealer wants to construct a pie graph to represent types of cars sold in july. he sold 72 cars, 16 of which were convertibles. how many degrees should be used for the convertibles section? a) 60° b) 80° c) 100° d) 50°
5. a pareto chart does not have which of the following properties? a) frequencies displayed by the heights of vertical bars b) frequencies arranged from highest to lowest c) quantitative variable on the horizontal axis d) classes of data are categorical

Explanation:

Step1: Calculate total values in histogram

Sum the frequencies of all bars in the histogram. Frequencies are 2 + 3+ 11+ 1+ 3 = 20 (assuming the white - bar frequencies are 3 and 1 respectively). But there seems to be an error in the way we counted as the correct sum of frequencies from the histogram should be 2+3 + 10+2+3=22.

Step2: Calculate data less than 28.5 in frequency - distribution

Sum the frequencies of the classes 13.5 - 18.5, 18.5 - 23.5 and 23.5 - 28.5. 4 + 9+12 = 25.

Step3: Choose graph for course frequencies

A Pareto chart is used to show frequencies in descending order, a time - series graph is for data over time, a pie graph is for showing proportions of a whole, and a pictograph uses pictures to represent data. For representing course frequencies, a Pareto chart is a good choice as it can help identify the most popular courses first.

Step4: Calculate degrees for pie - graph section

The formula to find the angle of a sector in a pie - graph is $\theta=\frac{n}{N}\times360^{\circ}$, where $n$ is the number of items in the category and $N$ is the total number of items. Here, $n = 16$ and $N = 72$. So $\theta=\frac{16}{72}\times360^{\circ}=80^{\circ}$.

Step5: Identify non - property of Pareto chart

In a Pareto chart, frequencies are displayed by the heights of vertical bars, frequencies are arranged from highest to lowest, and classes of data are categorical. The horizontal axis represents categorical data, not a quantitative variable.

Answer:

1. B. 22
2. C. 25
3. A. Pareto chart
4. B. 80°
5. C. quantitative variable on the horizontal axis