Question

which two data sets appear to be normally distributed?
a.

value	5	10	15	20	25	30	35	40	45	50	55
frequency	10	27	40	60	75	100	80	55	35	30	11

b.

value	5	10	15	20	25	30	35	40	45	50	55
frequency	11	17	23	29	35	41	47	53	59	65	71

c.

value	5	10	15	20	25	30	35	40	45	50	55
frequency	12	25	32	41	68	75	66	52	35	26	13

d.

value	5	10	15	20	25	30	21	24	27	30	33
frequency	13	18	23	28	33	38	43	48	53	58	63

Explanation:

A normal distribution has a symmetric bell - shaped curve. For a frequency distribution table, this means that the frequencies increase to a maximum and then decrease symmetrically.

• Option A: The frequencies increase (10, 27, 40, 60, 75, 100) and then decrease (80, 55, 35, 30, 11) in a somewhat symmetric fashion around the value of 30.
• Option C: The frequencies increase (12, 25, 32, 41, 68, 75) and then decrease (66, 52, 35, 26, 13) in a somewhat symmetric fashion around the value of 30.
• Option B: The frequencies are increasing throughout (11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71), so it is not symmetric and not a normal distribution.
• Option D: The data set has inconsistent value increments (21, 24, 27 etc. after 30) and the frequency pattern does not show the characteristic symmetric increase - decrease of a normal distribution.

Answer:

A. Option A, C.