Which scenario represents a statistical investigation? — Measuring the lengths of fish in a lake to study the fish population.Fish vary in length — measuring many fish creates a distribution to analyze. This is a classic statistical investigation!
A doctor asks: "What is the average blood pressure of adults ages 40-60?" This is statistical because: — Different adults have different blood pressures.Adults have varying blood pressures. Collecting data from many people creates a statistical distribution to analyze.
A student asks: "What score did I get on the test?" vs. "What scores did the class get?" Which is statistical and why? — Second is statistical (different students got different scores).The first has ONE answer (your score). The second has MANY answers that vary — making it statistical.
Surveys, experiments, and observational studies all generate statistical data because: — They collect data from multiple subjects, creating variation.All three methods collect data from MULTIPLE subjects or observations — creating the variation that statistics analyzes.
Which statistical question is most precisely defined? — How many hours do 8th graders in US public schools sleep on school nights?.Good statistical questions specify WHO (8th graders in US public schools), WHAT (hours of sleep), and WHEN (school nights). This precision makes the data collectible and comparable.
"The Earth is approximately 4.5 billion years old." Is this a statistical question? Why? — No — there is one objective answer (though measured with uncertainty).The Earth has one actual age. While measurements have uncertainty, the question has one "correct" answer — making it NON-statistical.
Which would generate a BIMODAL distribution (two peaks)? — Heights of both professional basketball players AND jockeys (horse racing) combined.Basketball players are very tall; jockeys are very short. Combining both creates TWO peaks in the distribution — bimodal! This is from the variability between groups.
A quality control engineer measures the weights of 1,000 candy bars. This is statistical because: — Manufacturing variation causes slightly different weights — collecting data reveals the distribution.Manufacturing processes cause tiny VARIATIONS in candy bar weights. Measuring 1,000 reveals the distribution of these variations — classic statistics!
The key question to ask yourself: "Is this statistical or not?" is: — "Would different observations/samples give different answers?".The golden rule: "Would different observations give different answers?" YES = statistical. NO (one universal answer) = not statistical.
A data set: 5, 5, 5, 5, 5. Mean, median, and mode are all: — All equal to 5.When all values are equal, mean = median = mode = that value = 5.
Adding 10 to every value in a data set changes the mean by: — +10.Adding a constant k to every value increases the mean by k. New mean = old mean + 10.
Multiplying every value by 3 multiplies the mean by: — 3.Multiplying every value by k multiplies the mean by k. New mean = 3 × old mean.
MAD (Mean Absolute Deviation) measures: — The average distance of each value from the mean.MAD = average of |each value − mean|. A small MAD means data clusters near the mean; large MAD means data is spread out.
Data: 4, 7, 7, 9, 13. Mean = 8. MAD = ? — 2.8.Deviations from mean 8: |4−8|=4, |7−8|=1, |7−8|=1, |9−8|=1, |13−8|=5. MAD = (4+1+1+1+5)/5 = 12/5 = 2.4.
When are mean and median EQUAL? — When the distribution is symmetric (no skew).Mean and median are equal when the distribution is perfectly SYMMETRIC — data is evenly spread around the center.
A store's daily sales for 5 days: $120, $150, $130, $160, $?. The mean is $140. What is the 5th day's sales? — $140.Sum = 140×5 = 700. Known sum = 120+150+130+160 = 560. 5th day = 700−560 = $140.
A bimodal data set has: — Two modes (two values with equal highest frequency).BIMODAL = two values that both appear the most frequently (tied for highest frequency).
Why might you prefer MEDIAN over MEAN for household income data? — A few very high incomes (outliers) pull the mean up, making median more representative.Very high incomes (billionaires) are outliers that inflate the mean significantly. The median represents the "typical" household better, as it is not affected by extremes.
A data set is right-skewed (long tail to the right). Where does the mean sit relative to the median? — Mean > Median.Right skew means a few very HIGH values pull the mean to the RIGHT (higher than the median). Mean > Median in right-skewed data.
Box Plot A: IQR = 15. Box Plot B: IQR = 4. Which data set is MORE spread out in the middle? — Box Plot A (IQR=15).Larger IQR = more spread out middle 50%. Box Plot A (IQR=15) is more spread out.
Data: 2,4,4,6,8,10,10,12. Five-number summary — Median = ? — 7.8 values. Middle two: 4th=6 and 5th=8. Median = (6+8)/2 = 7.
Same data (2,4,4,6,8,10,10,12). Q1 = ? — 4.Lower half: 2,4,4,6. Median = (4+4)/2 = 4 = Q1.
A histogram has 5 bars. The y-axis shows frequency. Reading the histogram tells you the: — Shape of the distribution and frequency per interval.Histograms show the SHAPE of the distribution (symmetric/skewed) and how many values fall in each interval.
An outlier rule: a value is an outlier if it is more than 1.5 × IQR beyond Q1 or Q3. If Q1=10, Q3=22, IQR=12: lower fence = ? — −8.Lower fence = Q1 − 1.5×IQR = 10 − 1.5×12 = 10 − 18 = −8. Values below −8 are outliers.
Which display shows if a data set is symmetric vs. skewed? — Histogram OR box plot OR dot plot (all can show shape).ANY graphical display (histogram, box plot, dot plot) can show whether data is symmetric or skewed by revealing the distribution shape.
A box plot whisker extends much further on the right than the left. This indicates: — Right-skewed data (longer right whisker = outliers/extreme high values).A long RIGHT whisker means the data extends far to the right (high end) — classic sign of RIGHT-SKEWED data.