Statistics & Probability

Cumulative frequency (ogive) graphs display the running total of observations, allowing you to locate the value corresponding to any cumulative proportion; the 50% point gives the median and the 25% and 75% points give the lower and upper quartiles, so answer C is correct. The mode is not read directly because an ogive shows cumulative, not individual, frequencies, making option A a trap.

A strong positive correlation on a scatter plot means the points lie close to an upward‑sloping line, indicating that higher values of one variable are associated with higher values of the other, so answer C is correct. The choice that the variables decrease together describes a negative correlation, which is the opposite pattern and therefore incorrect.

The mean of four numbers is total sum divided by 4; setting (6+8+x+10)/4 = 9 gives 6+8+x+10 = 36, so x = 36−24 = 12, which matches answer B. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Answer A (10) arises from forgetting to include all four terms in the sum, which would give a total of 30 and a mean of 7.5, not the required 9.
• !The choice 7 is a common trap because it is the third term, not the central value, and therefore does not split the data into equal halves.
• !A common wrong answer is 0.30, which results from mistakenly adding the probabilities (0.4+0.3) instead of multiplying, which only applies to mutually exclusive events, not independent ones.
• !The mode is not read directly because an ogive shows cumulative, not individual, frequencies, making option A a trap.
• !The choice that the variables decrease together describes a negative correlation, which is the opposite pattern and therefore incorrect.

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