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:

Step1: Recall normal - distribution property

A normal - distribution has a bell - shaped curve, with frequencies increasing to a maximum at the mean and then decreasing symmetrically on either side.

Step2: Analyze dataset A

The frequencies in dataset A increase from 10 to 100 and then decrease symmetrically (10, 27, 40, 60, 75, 100, 80, 55, 35, 30, 11), which is characteristic of a normal distribution.

Step3: Analyze dataset B

The frequencies in dataset B (11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71) are increasing in a linear fashion and do not show the bell - shaped pattern of a normal distribution.

Step4: Analyze dataset C

The frequencies in dataset C increase from 12 to 75 and then decrease symmetrically (12, 25, 32, 41, 68, 75, 66, 52, 35, 26, 13), which is characteristic of a normal distribution.

Step5: Analyze dataset D

Dataset D has some non - sequential values in the 'value' column and the frequency pattern does not show the characteristic bell - shaped curve of a normal distribution.

Answer:

A. Dataset A
C. Dataset C