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Critical Thinking Consider these types of graphs: histogram, bar graph. Pareto chart, pie chart, stem-and-leaf display.
(a) Which are suitable for qualitative data?
(b) Which are suitable for quantitative data?
(a)
![Check Mark](/static/check-mark.png)
Whether the graph types histogram, bar graph, Pareto chart, Pie chart, and stem-and-leaf are suitable for qualitative data.
Answer to Problem 1CR
Solution: The graph types bar graph, Pareto chart, and Pie chart are suitable for qualitative data.
Explanation of Solution
Qualitative data involves categories that are not numerical, such as eye color, type of coffee bean, and species of birds seen in a garden. The only numbers that can be related to these categories are frequencies, so only charts with one numerical axis can be used. It can be represented through pictures that explore the data in a visual way and visual representations focus on the themes found in the data.
Bar graph and Pareto chart are a way to visually represent
Pie chart graph is helpful when graphing
The graph types bar graph, Pareto chart, and Pie chart are suitable for qualitative data.
(b)
![Check Mark](/static/check-mark.png)
Whether the graph types histogram, bar graph, Pareto chart, Pie chart, and stem-and-leaf are suitable for quantitative data.
Answer to Problem 1CR
Solution: All graph types histogram, bar graph, Pareto chart, Pie chart, and stem-and-leaf are suitable for quantitative data.
Explanation of Solution
Quantitative data is information about quantities, that is, information that can be measured and written down with numbers.
A
A Bar graph is a diagram in which the numerical values of variables are represented by the height or length of lines or rectangles of equal width. In Pareto graph, data are displayed either horizontally or vertically and allow viewers to compare items, such as amounts, characteristics, times, and frequency.
A
A pie chart is a circular chart used to compare parts of the whole. It is divided into sectors that are equal in size to the quantity represented.
All graph types are suitable for quantitative data.
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Chapter 2 Solutions
Student Solutions Manual for Brase/Brase's Understanding Basic Statistics, 7th
- Let X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).arrow_forwardA well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward
- 8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward
- 9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward
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