Download NWCA Frequency Distributions and Graphs Exam and more Exams Technology in PDF only on Docsity!
Exam
Question 1. Which scale of measurement allows for meaningful statements about both differences and ratios between values? A) Nominal B) Ordinal C) Interval D) Ratio Answer: D Explanation: Ratio scales have a true zero, permitting statements about how many times larger one value is than another, unlike interval scales. Question 2. A researcher counts the number of cars that pass a checkpoint each hour. This variable is best classified as: A) Nominal B) Ordinal C) Discrete D) Continuous Answer: C Explanation: The count of cars is a whole‑number quantity; it cannot be fractioned, making it discrete. Question 3. When converting raw data into a frequency table, the term “frequency” ($f$) refers to: A) The total number of observations B) The number of times a particular value or class occurs C) The proportion of a class relative to the sample size D) The midpoint of a class interval
Exam
Answer: B Explanation: Frequency is the count of observations that fall within a specific value or class. Question 4. In a categorical frequency distribution, which of the following is NOT a required component? A) Class limits B) Category names C) Frequencies for each category D) Total sample size Answer: A Explanation: Categorical data use distinct categories, not class limits, which apply to grouped numerical data. Question 5. An ungrouped frequency distribution is most appropriate when: A) The data range is extremely large B) The data are nominal C) The number of distinct values is relatively small D) The researcher wants to create a histogram Answer: C Explanation: Ungrouped tables list each distinct value; they are practical only when there are few unique values. Question 6. For a grouped frequency distribution, the lower class limit of the first class is 12 and the class width is 5. What is the upper class limit of the third class? A) 22 B) 27
Exam
B) Touch each other C) Vary in width arbitrarily D) Be colored differently for each class Answer: B Explanation: For continuous data, adjacent bars must touch to reflect the uninterrupted nature of the scale. Question 10. When drawing a frequency polygon, the graph is “anchored” to the horizontal axis by: A) Adding a point at the first class midpoint with frequency zero B) Adding a point at the last class midpoint with frequency zero C) Adding points at both the first and last class boundaries with frequency zero D) Connecting the highest frequency point to the axis Answer: C Explanation: Anchoring uses zero‑frequency points at the lower boundary of the first class and the upper boundary of the last class. Question 11. An ogive plots cumulative frequency against: A) Class midpoints B) Lower class limits C) Upper class boundaries D) Relative frequencies Answer: C Explanation: The ogive uses the upper class boundary on the horizontal axis to show the running total of frequencies.
Exam
Question 12. Which of the following best describes a Pareto chart? A) A pie chart sorted alphabetically B) A bar chart of categories arranged in descending order of frequency, often with a cumulative line C) A histogram with unequal class widths D) A time‑series line graph Answer: B Explanation: Pareto charts emphasize the most significant categories by ordering bars from highest to lowest frequency and frequently include a cumulative percentage line. Question 13. In a time‑series graph, the horizontal axis typically represents: A) Frequency B) Cumulative frequency C) Time intervals D) Class midpoints Answer: C Explanation: Time‑series graphs track changes over chronological periods, so the x‑axis shows time. Question 14. To calculate the angle for a slice in a pie chart representing a class with frequency 15 out of a total of 60, you use: A) $(15/60) \times 180^\circ$ B) $(15/60) \times 360^\circ$ C) $(60/15) \times 360^\circ$ D) $(15/60) \times 90^\circ$ Answer: B
Exam
Explanation: The modal class is simply the class interval that contains the most observations. Question 18. To estimate the mean from grouped data, which of the following steps is essential? A) Use the class boundaries instead of limits B) Multiply each class midpoint by its frequency, sum the products, then divide by $n$ C) Add the lower limits of all classes and divide by the number of classes D) Use the median of the class midpoints Answer: B Explanation: The grouped‑data mean estimate = $\displaystyle \frac{\sum (X_m \cdot f)}{n}$. Question 19. A graph that appears to exaggerate differences by truncating the vertical axis is an example of: A) A Pareto chart B) A misleading graph C) An ogive D) A stem‑and‑leaf plot Answer: B Explanation: Truncating the y‑axis can inflate visual differences, leading to misinterpretation. Question 20. If the class width is 7 and the lower limit of the first class is 3, what is the lower limit of the fourth class? A) 17 B) 20 C) 24 D) 31
Exam
Answer: B Explanation: Each successive lower limit adds the width: 3, 10, 17, 24 → actually the fourth lower limit is 24 (answer C). Question 21. Which of the following statements about interval data is FALSE? A) It has equal distances between adjacent values B) It possesses a true zero point C) Arithmetic operations like addition are meaningful D) Temperature in Celsius is an example Answer: B Explanation: Interval scales lack a non‑arbitrary zero; thus ratios are not meaningful. Question 22. When constructing class boundaries, you typically add or subtract 0.5 to the class limits when the data are: A) Discrete B) Continuous and measured to the nearest whole number C) Nominal D) Ordinal Answer: B Explanation: Adding 0.5 adjusts for measurement precision, ensuring boundaries correctly separate adjacent intervals. Question 23. In a cumulative frequency table, the cumulative frequency for the last class always equals: A) The class width B) The total sample size $n$
Exam
Question 26. Which of the following best defines “raw data management”? A) Summarizing data into percentages only B) Transforming unorganized observations into a structured frequency table C) Creating graphs before any calculations D) Removing outliers without documentation Answer: B Explanation: Raw data management involves organizing raw observations into a systematic format such as a frequency table. Question 27. In a histogram, the area of each bar is proportional to: A) The relative frequency of the class B) The absolute frequency of the class C) The class width only D) The cumulative frequency Answer: A Explanation: For histograms of continuous data, bar area (height × width) represents relative frequency; height alone represents frequency per unit width. Question 28. Which of the following is a correct interpretation of a positively skewed distribution? A) Mean = Median = Mode B) Mean > Median > Mode C) Mean < Median < Mode D) Median = Mode > Mean Answer: B
Exam
Explanation: In a right‑skewed (positive) distribution, the mean is pulled toward the tail, making it larger than the median, which in turn exceeds the mode. Question 29. If a frequency polygon and a histogram are drawn for the same data set, the polygon will: A) Always lie above the histogram B) Always lie below the histogram C) Pass through the midpoints of the tops of the histogram bars D) Have a different shape altogether Answer: C Explanation: Frequency polygons connect points at the class midpoints whose vertical coordinate equals the class frequency. Question 30. The purpose of a “cumulative relative frequency” plot (Ogive) is to: A) Show the proportion of data below a particular value B) Display the frequency of each class separately C) Highlight the most frequent category D) Compare two unrelated data sets Answer: A Explanation: Cumulative relative frequency indicates the fraction of observations that fall at or below each upper class boundary. Question 31. When converting a grouped frequency distribution into a stem‑and‑leaf plot, the “stem” typically represents: A) The class frequency B) The leading digit(s) of the data values
Exam
A) The mean age is exactly 32 B) No other class has a frequency greater than 45 C) The median age must lie in this class D) The class width is 5 Answer: B Explanation: By definition, the modal class has the highest frequency; other classes cannot exceed 45. Question 35. Which graph would be most misleading if the y‑axis were truncated to start at 20 instead of 0 for a histogram displaying frequencies ranging from 0 to 50? A) Pie chart B) Histogram C) Stem‑and‑leaf plot D) Time‑series line graph Answer: B Explanation: Truncating the y‑axis in a histogram exaggerates differences between bars, potentially misleading the viewer. Question 36. The relative frequency for a class with $f = 12$ and $n = 80$ is: A) 0. B) 0. C) 6.67% D) 12% Answer: A Explanation: $rf = f/n = 12/80 = 0.15$ (or 15%).
Exam
Question 37. In constructing class boundaries, why is it necessary to add 0.5 (or half the smallest unit of measurement) to the upper limit? A) To increase the class width B) To avoid overlapping intervals C) To ensure that each data value falls into exactly one class when measurements are recorded to the nearest whole number D) To convert discrete data to continuous data Answer: C Explanation: Adding 0.5 creates a boundary that separates adjacent whole‑number values, ensuring proper allocation. Question 38. Which of the following best describes a “uniform” distribution shape? A) All classes have approximately the same frequency B) Frequencies increase then decrease symmetrically C) There is a long tail to the right D) The distribution is heavily peaked in the center Answer: A Explanation: In a uniform distribution, each interval occurs with roughly equal frequency. Question 39. When estimating the mean from grouped data, which of the following errors will most affect the estimate? A) Using class boundaries instead of limits B) Rounding class midpoints to the nearest integer C) Forgetting to multiply by class width D) Ignoring the cumulative frequency column Answer: B
Exam
D) Frequency multiplied by class midpoint Answer: B Explanation: Width = difference between successive lower limits (or upper limits), assuming equal spacing. Question 43. Which of the following would most likely be displayed using a histogram rather than a bar chart? A) Number of students in each grade level (freshman, sophomore, junior, senior) B) Distribution of test scores ranging from 0 to 100 C) Preference for three brand colors D) Count of countries by continent Answer: B Explanation: Histograms are used for continuous numerical data such as test scores. Question 44. The cumulative frequency for the class “15‑ 19 ” is 120, and the total sample size is 200. What is the cumulative relative frequency for this class? A) 0. B) 0. C) 0. D) 0. Answer: B Explanation: Cumulative relative frequency = 120/200 = 0.60. Question 45. When a data set exhibits a “negative skew,” which of the following statements is true? A) Mean < Median < Mode
Exam
B) Mean > Median > Mode C) Mean = Median = Mode D) Median = Mode > Mean Answer: A Explanation: In left‑skewed (negative) distributions, the tail is on the left, pulling the mean below the median and mode. Question 46. If a researcher groups ages into 5‑year intervals starting at 0 (0‑4, 5‑9, …) and records a frequency of 0 for the first interval, what does this indicate? A) Data were incorrectly entered B) No subjects were younger than 5 years old C) The class width should be increased D) The distribution is negatively skewed Answer: B Explanation: A frequency of zero simply means no observations fell into that interval. Question 47. Which of the following best explains why gaps are present between bars in a bar chart but not in a histogram? A) Bar charts display categorical data; histograms display continuous data B) Histograms are always drawn in color C) Bar charts require equal class widths D) Histograms use relative frequencies only Answer: A Explanation: Gaps emphasize that categories are distinct; continuous data in histograms have no gaps because the intervals are adjacent.
Exam
Answer: B Explanation: Percentage = relative frequency × 100 = $(f/n) \times 100$. Question 51. When constructing a grouped frequency table, the decision to use 6 versus 7 classes primarily affects: A) The total sample size B) The level of detail (granularity) in the distribution C) The type of graph that can be drawn D) The measurement scale of the data Answer: B Explanation: More classes provide finer detail but may result in sparse frequencies; fewer classes give a broader overview. Question 52. In a cumulative frequency graph, a steep slope between two points indicates: A) A large increase in cumulative frequency over a short interval (high density of data) B) A decrease in frequency C) An error in data entry D) Uniform distribution Answer: A Explanation: A steep segment shows many observations accumulating quickly within that range. Question 53. Which of the following best describes the relationship between the mean and median in a perfectly symmetrical (normal) distribution? A) Mean > Median B) Mean < Median C) Mean = Median
Exam
D) No consistent relationship Answer: C Explanation: In a symmetric distribution, the mean and median coincide at the center. Question 54. If the class limits for a class are 10 and 19, what are the class boundaries assuming data are recorded to the nearest integer? A) 9.5 – 19. B) 10 – 19 C) 9.5 – 19 D) 10 – 19. Answer: A Explanation: Subtract 0.5 from lower limit and add 0.5 to upper limit: 9.5 – 19.5. Question 55. A frequency distribution shows that the cumulative frequency reaches 150 at the upper boundary of 30. If the total sample size is 200, what percentage of observations are ≤30? A) 60% B) 70% C) 75% D) 80% Answer: C Explanation: 150/200 = 0.75 → 75%. Question 56. Which of the following is a reason to prefer a histogram over a frequency polygon? A) Histograms display the exact shape of the distribution without approximation
