Graphs & Displays
Identify whether a bar graph, line graph, or circle graph is best: You want to show how students in a class choose their favorite sport (soccer, basketball, baseball). Which graph do you choose and why?
Bar Graph
Define a frequency table.
A table that lists data values and how often each occurs.
Give the definition of mean, median, and mode (one phrase each).
Mean: average; Median: middle value; Mode: most frequent value.
Define experimental probability in one sentence
Experimental probability = observed frequency of an event divided by total trials.
Define theoretical probability in one sentence.
Theoretical probability = number of favorable outcomes divided by total possible equally likely outcomes.
Given a small table of monthly temperatures (Jan: 30, Feb: 32, Mar: 45, Apr: 55), describe how you would display them on a line graph (list axes, labels, and a brief sketch idea).
x-axis: months; y-axis: temperature; plot points and connect with lines.
Create a frequency table for these test scores: 78, 85, 78, 90, 85, 92.
Frequency — 78:2, 85:2, 90:1, 92:1.
ind the mean, median, and mode for: 12, 15, 15, 18, 20.
Mean = (12+15+15+18+20)/5 =16; Median = 15; Mode = 15.
ou flip a coin 40 times and get 26 heads. What is the experimental probability of heads? Use fraction and decimal (rounded to 2 decimals).
26/40 =0.65 (decimal 0.65).
What is the theoretical probability of rolling a 4 on a fair six-sided die? Give a fraction and a decimal.
0.1667
"A pie chart shows the market share of three companies as 10%, 10%, and 80%." Explain why this pie chart could be misleading.
Misleading because tiny categories (10%, 10%) appear much smaller than 80% — might be fine numerically but labeling or removing scale/3D effects could mislead.
Use the frequency table above to draw (describe) a histogram: list bins you would use and the bar heights.
Bins: 75–79:2, 80–84:0, 85–89:2, 90–94:2; bar heights equal frequencies.
Explain how an outlier affects the mean and the median. Give a numeric example (brief).
Outlier pulls the mean toward it; the median is unchanged if the outlier is at an extreme. Example: {10,11,12,13,100} mean = 1465=29.25146=29.2, median = 12.
Describe how you would use a simulation (e.g., die rolls or random number generator) to estimate the probability of drawing a red card from a shuffled standard deck (ignore suits beyond color).
Simulate by repeatedly shuffling and drawing one card, record the color, repeat many times, and compute the frequency of red.
Two fair coins are flipped. List the sample space and find the probability of getting exactly one head.
Sample space: {HH, HT, TH, TT}; exactly one head = {HT, TH} so probability 2/4=1/2
You have survey counts for favorite school lunch items by grade (4 grades). Explain when a stacked bar chart is better than separate bar graphs, and give one drawback of stacked bars.
Stacked bar shows parts of whole by grade and allows comparison of totals; drawback: hard to compare individual categories across bars.
Explain step-by-step how to create a stem-and-leaf plot for these values: 63, 67, 71, 74, 74, 79, 82.
Stem: 6|3,7; 7|1,4,4,9; 8|2 (show stems 6,7,8 and leaves sorted).
The data set of 7 numbers has median 40. Explain how you would estimate the mean if you only know the five middle numbers and that the two extremes differ greatly.
Use interquartile info from the middle five to estimate the mean roughly, but note uncertainty; recommend collecting full data or using trimmed mean.
After running an experiment to estimate the probability that a spinner lands on red, your observed frequency differs from the theoretical probability. List three possible reasons for the discrepancy.
Possible reasons: small sample size, biased process or tool, human error in recording.
A bag contains 3 red, 4 blue, and 5 green marbles. If one marble is drawn at random, what is the probability it is not blue? Show fraction and percent.
Not blue = red + green = 3+5 = 8 out of total 12 → 8/12=2/3≈66.67%
Given a data set with categories that overlap (e.g., students who play soccer and music), explain why a circle graph might be inappropriate and name two better display options with reasons.
Because categories overlap, a pie chart assumes disjoint parts; use a Venn diagram or a stacked/clustered bar chart.
Given raw data with outliers (e.g., most values near 50, one value 500), explain how a histogram and a stem-and-leaf plot each help reveal the outlier and which display better shows exact values.
A histogram highlights distribution shape and outlier as a tall/isolated bar; a stem-and-leaf shows exact values, so it reveals the outlier's exact value.
Describe how to construct a box-and-whisker plot from a data set and explain what each part (box, median line, whiskers) represents.
Order data, find median (Q2), find Q1 (median of lower half) and Q3 (median of upper half), draw box from Q1 to Q3 with median line; whiskers extend to min and max (or to 1.5*IQR rule if showing outliers separately).
Design a brief experiment (materials and steps) for students to collect data to approximate the probability that a tossed paper cup lands open-end up. Explain how to use the results to make a prediction.
Example: Materials — plastic cup, flat surface; Steps — toss cup 100 times, record counts open-end up/down; experimental probability = open-up count / 100; use to predict future proportion with margin for sample variation.
Explain the difference between independent and dependent events. Give one example of each in a classroom context and compute a theoretical probability for one of them.
Independent: outcome of one event doesn't affect the other (e.g., flipping two different fair coins). Dependent: first draw without replacement affects second (e.g., drawing two marbles without replacement). Example compute (independent) probability of getting heads twice = 1/2×1/2=1/4