Frequency distribution curves (i). Having a single hump, are called as unimodal curves. (ii). If symmetrical, are called as normal curves. (iii). If unsymmetrical, are called as skew curves.
- AOnly (i)
- B(i) and (ii)
- C(ii) and (iii)
- D(i), (ii) and (iii)Correct
Solution
Concept
A frequency distribution curve shows how data values are spread. Its shape depends on the number of peaks and whether it is balanced or tilted.
Step-by-step solution
1. Statement (i) says curves with a single hump (one peak) are unimodal curves. A peak represents the mode. So one peak means unimodal. This statement is correct. 2. Statement (ii) says symmetrical curves are called normal curves. A symmetrical bell-shaped curve is known as a normal curve. This statement is correct. 3. Statement (iii) says unsymmetrical curves are called skew curves. When data leans more to one side, it has skewness. So unsymmetrical curves are skew curves. This statement is correct. 4. Since all three statements are true, the correct combination is (i), (ii) and (iii). Answer: (D) (i), (ii) and (iii)
Explanation
A unimodal curve has only one peak or highest frequency. A normal distribution curve is perfectly symmetrical about its mean. An asymmetrical frequency curve is skewed either to the left or right, so it is called a skew curve.
Why the other options are wrong
A: It ignores statements (ii) and (iii), which are also standard correct definitions. B: It leaves out statement (iii), but unsymmetrical curves are indeed called skew curves. C: It leaves out statement (i), but single-hump curves are correctly called unimodal curves.
Shortcut
Remember: 'Uni' means one peak (unimodal), 'symmetric' gives a normal bell curve, and 'asymmetric' means skewed.
Common mistake
Students sometimes think all symmetrical curves must be called something else, but in basic statistics, symmetrical bell-shaped frequency curves are standard normal curves.
Correct answer: D) (i), (ii) and (iii)