Questions: Question 4 The IQ scores of 50 students are given below. 89 88 112 100 109 99 99 112 93 95 107 106 102 106 101 97 98 112 94 110 93 91 114 117 107 113 86 117 108 90 91 98 87 117 114 101 95 101 87 99 97 110 88 117 86 109 104 119 93 105 (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 90 - 94 95 - 99 100 - 104 105 - 109 110 - 114 115 - 119 (b) Which of the following is the correct histogram for this data?

Question 4

The IQ scores of 50 students are given below.

89 88 112 100 109 99 99 112 93 95 107 106 102 106 101 97 98 112 94 110 93 91 114 117 107 113 86 117 108 90 91 98 87 117 114 101 95 101 87 99 97 110 88 117 86 109 104 119 93 105

(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 90 - 94 95 - 99 100 - 104 105 - 109 110 - 114 115 - 119

(b) Which of the following is the correct histogram for this data?

Transcript text: Question 4 The IQ scores of 50 students are given below. 89 88 112 100 109 99 99 112 93 95 107 106 102 106 101 97 98 112 94 110 93 91 114 117 107 113 86 117 108 90 91 98 87 117 114 101 95 101 87 99 97 110 88 117 86 109 104 119 93 105 (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 90 - 94 95 - 99 100 - 104 105 - 109 110 - 114 115 - 119 (b) Which of the following is the correct histogram for this data?

Solution

Solution Steps

Step 1: Create the frequency distribution table

The data ranges from 86 to 119. We're told to use 85-89 for the first class and the same width for subsequent classes. The class width is \(89-85+1 = 5\). Therefore the classes are 85-89, 90-94, 95-99, 100-104, 105-109, 110-114, and 115-119. Count the number of data points that fall into each class:

| Class | Frequency | |---|---| | 85 - 89 | 2 | | 90 - 94 | 7 | | 95 - 99 | 9 | | 100 - 104 | 7 | | 105 - 109 | 8 | | 110 - 114 | 6 | | 115 - 119 | 4 |

Step 2: Create the histogram

The histogram visually represents the frequency distribution. The x-axis represents the classes and the y-axis represents the frequency. Each bar's height corresponds to the frequency of its respective class.

Step 3: Choose the correct histogram

The correct histogram should match the frequency distribution table we created. From the image, the provided histogram has the correct bar heights matching the frequencies in the table.

Final Answer

a) | Class | Frequency | |---|---| | 85 - 89 | 2 | | 90 - 94 | 7 | | 95 - 99 | 9 | | 100 - 104 | 7 | | 105 - 109 | 8 | | 110 - 114 | 6 | | 115 - 119 | 4 | b) The histogram shown in the image is correct.

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