Quiz with Solutions: Chapter 2 (17 min)

These solutions show about the same level of work I expect from you, though I add quite a bit of extra commentary. Please see Show Your Work for the what, why, and how.

Answer: categorical
(also acceptable: attribute or qualitative)

Answer: Any two of:
histogram bars touch and bar graph bars don’t
histogram shows numeric data and bar graph shows qualitative data
histogram has only one possible order but bar graph can have any order

Remark:  There’s another difference, but you can’t use it for this question. For both a bar chart and an ungrouped frequency histogram, you label the x axis at the centers of the bars. But for a grouped frequency histogram, you label the x axis at the edges of the bars, which are the boundaries of the classes. This is one way in which ungrouped frequency histograms are like bar graphs but different from grouped frequency histograms.

3(points: 3) Identify the shapes of these histograms, using the most specific terms that we learned:
     

Answer:  See page 80 of your textbook.
(a) bell shaped (or symmetric)    (b) skewed right (c) uniform

(Q4–Q6) Here are 19 exam scores:

76 74 82 96 66 76 78 72 52 68 86 84 62 76 78 92 82 74 88

Answer:  See pages 76–77 in your textbook.

        5 | 2
        6 | 6 8 2
        7 | 6 4 6 8 2 6 8 4
        8 | 2 6 4 2 8
        9 | 6 2

Your classes will be 50–59, 60–69, 70–79, and so on. Luckily, you’ve already split the numbers into those classes in making the stem plot above, so you don’t need to tally the data again in making the histogram.

Answer: 

Common mistake:  mislabeling the x axis by putting class limits 50–59, 60–69, etc. below the centers of the bars. You label the centers of the bars for a bar graph (categorical data) or for an ungrouped frequency histogram. For a grouped histogram you show the class boundaries. Please refer to examples on page 83.

Remark: It’s not actually wrong, but when you are creating a frequency histogram there’s no need to compute all the relative frequencies.

Remark: In the picture, I labeled the vertical axis every two units, but some students labeled it every one unit. That’s just fine when the maximum frequency is fairly small, as it is in this example.

Answer:  (c) 3/19 ≈ 0.158 or 15.8%

Remark: The computation is (frequency of the class you’re interested in) divided by (sample size, or sum of all frequencies”.) Here there are five numbers in the 80–89 class, and 19 numbers in the whole sample.

Common mistake: A common mistake is dividing upside down, 19/3. The relative frequency must always be a percentage ≤100% or a decimal ≤1.00.