Decision and conditions
Read frequencies and describe position or dispersion using the stated definition. Percentile convention is stated explicitly. A normal-model probability is supplied rather than assumed from an arbitrary data set.
Worked model
A data set consists of 3 occurring twice, 4 occurring five times, and 7 occurring three times. What is its mode? The frequencies are 2, 5 and 3. The frequency 5 is greatest. The mode is its associated value, 4. Before calculating: Find the value with greatest frequency, rather than the greatest value.
Contrast: a different decision
Among 20 distinct scores sorted increasingly, a score is in position 7. Define its percentile rank as 100 times the fraction of scores strictly below it. What is its percentile rank? There are 6 lower scores. The fraction is that count divided by 20. The percentile rank is 100(6)/20 = 30. Before calculating: Strictly below excludes the score itself.
Transfer with solution
A data set has standard deviation 3. Every observation is multiplied by −3, then increased by 7. What is the new standard deviation? Multiplying every deviation by −3 multiplies its magnitude by 3. Adding a common constant changes no deviation from the mean. The standard deviation becomes 9. Before calculating: Separate the effect of scaling deviations from the effect of translating all values.
Check the boundary
A percentage below a value is not the value itself, and scaling differs from translating. X is normally distributed with mean 30 and standard deviation 3. Given P(X < 33) = 0.8413, what is P(27 < X < 33)? Symmetry gives the lower-tail probability 1 − 0.8413 = 0.1587. Subtract that lower tail from the cumulative probability at the upper cutoff. The central probability is 0.8413 − 0.1587 = 0.6826.
A data set consists of 3 occurring twice, 4 occurring five times, and 7 occurring three times. What is its mode?
- The frequencies are 2, 5 and 3.
- The frequency 5 is greatest.
- The mode is its associated value, 4.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GRE Quantitative Reasoning overview