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 11b. value 5 10 15 20 25 30 35 40 45 50 55 frequency 11 17 23 29 35 41 47 53 59 65 71c. value 5 10 15 20 25 30 35 40 45 50 55 frequency 12 25 32 41 68 75 66 52 35 26 13d. 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 properties of normal distribution

A normal distribution is symmetric about the mean. The frequency first increases to a maximum (at the mean) and then decreases symmetrically.

Step2: Analyze dataset A

The frequencies are \(10,27,40,60,75,100,80,55,35,30,11\). The frequencies increase to \(100\) (at value \(30\)) and then decrease. The left - hand side frequencies (\(10,27,40,60,75\)) and right - hand side frequencies (\(80,55,35,30,11\)) show a symmetric - like pattern around the maximum frequency.

Step3: Analyze dataset C

The frequencies are \(12,25,32,41,68,75,66,52,35,26,13\). The frequencies increase to \(75\) (at value \(30\)) and then decrease. The left - hand side frequencies (\(12,25,32,41,68\)) and right - hand side frequencies (\(66,52,35,26,13\)) show a symmetric - like pattern around the maximum frequency.

Step4: Analyze dataset B

The frequencies \(11,17,23,29,35,41,47,53,59,65,71\) are increasing throughout. There is no decrease after a maximum, so it is not symmetric (not normal).

Step5: Analyze dataset D

The values are not in a proper order (\(5,10,15,20,25,30,21,24,27,30,33\)) and the frequency distribution does not follow the symmetric pattern of a normal distribution.

Answer:

A. Dataset A, C. Dataset C