Question

the iq scores of 50 students are given below.
97 112 99 118 118 101 93 119 118 91
85 95 93 91 117 117 104 95 112 113
119 86 117 92 111 113 113 117 115 111
117 108 100 113 110 88 89 91 98 95
117 94 101 104 104 107 85 113 115 116
(a) construct a grouped frequency distribution for the data. use 85 - 89 for the first class and use the same width for each subsequent class.
class frequency
85 - 89
(b) which of the following is the correct histogram for this data?

Explanation:

Step1: Determine class - width

The first class is 85 - 89, so the class - width is \(89 - 85=4\).

Step2: Define classes

The classes will be 85 - 89, 90 - 94, 95 - 99, 100 - 104, 105 - 109, 110 - 114, 115 - 119.

Step3: Count frequencies

• For the class 85 - 89: Count the number of scores in this range. The scores 85, 85, 86, 88, 89 are in this class. So the frequency is 5.
• For the class 90 - 94: The scores 91, 91, 91, 92, 93, 93, 94 are in this class. So the frequency is 7.
• For the class 95 - 99: The scores 95, 95, 95, 97, 98, 99 are in this class. So the frequency is 6.
• For the class 100 - 104: The scores 100, 101, 101, 104, 104, 104 are in this class. So the frequency is 6.
• For the class 105 - 109: The scores 107, 108 are in this class. So the frequency is 2.
• For the class 110 - 114: The scores 111, 111, 112, 113, 113, 113, 113, 113 are in this class. So the frequency is 8.
• For the class 115 - 119: The scores 115, 115, 116, 117, 117, 117, 117, 117, 118, 118, 119, 119 are in this class. So the frequency is 12.

The grouped - frequency distribution is:

Class	Frequency
90 - 94	7
95 - 99	6
100 - 104	6
105 - 109	2
110 - 114	8
115 - 119	12

Since part (b) of the question is not fully shown (no histogram options provided), we can only answer part (a).

Answer:

Class	Frequency
90 - 94	7
95 - 99	6
100 - 104	6
105 - 109	2
110 - 114	8
115 - 119	12