Question

the iq scores of 50 students are given below.
108 105 89 105 105 105 91 100 86 89
93 89 100 98 97 119 105 106 115 95
104 95 111 108 108 99 94 98 103 114
87 89 102 100 119 119 109 101 118 105
104 105 94 93 87 114 99 116 116 105
(a) construct a frequency distribution for the data. start with 85 as the lower limit of the first class and use a class width of 5.
class frequency
empty table with class and frequency columns, multiple empty rows for class intervals and frequencies

Explanation:

Step1: Determine class intervals

Start with lower limit 85, class width 5. So classes are: 85 - 89, 90 - 94, 95 - 99, 100 - 104, 105 - 109, 110 - 114, 115 - 119.

Step2: Count frequencies for each class

• 85 - 89: Values are 86, 87, 87, 89, 89, 89, 89. Count: 7.
• 90 - 94: Values are 91, 93, 93, 94, 94. Count: 5.
• 95 - 99: Values are 95, 95, 97, 98, 98, 99, 99. Count: 7.
• 100 - 104: Values are 100, 100, 100, 101, 102, 103, 104, 104. Count: 8.
• 105 - 109: Values are 105 (multiple times), 106, 108, 108, 108, 109. Let's count: 105 appears 7 times, 106,108(3),109. Total: 7+1+3+1=12? Wait, recheck: 105: let's list all 105s: first row 105,105,105,105; second row 105; fourth row 105; fifth row 105,105. Wait total 105s: 4 (row1) +1 (row2) +1 (row4) +2 (row5) = 8? Wait no, original data:

Row1: 108,105,89,105,105,105,91,100,86,89

Row2:93,89,100,98,97,119,105,106,115,95

Row3:104,95,111,108,108,99,94,98,103,114

Row4:87,89,102,100,119,119,109,101,118,105

Row5:104,105,94,93,87,114,99,116,116,105

So 105s: row1: 4 times (105,105,105,105), row2:1 (105), row4:1 (105), row5:2 (105,105). Total 4+1+1+2=8. Then 106:1, 108:3 (row3:108,108; row1:108), 109:1. So 8+1+3+1=13? Wait maybe I miscounted. Let's do better:

List all data points:

85-89: 86,87,87,89,89,89,89 (7)

90-94:91,93,93,94,94 (5)

95-99:95,95,97,98,98,99,99 (7)

100-104:100,100,100,101,102,103,104,104 (8)

105-109:105 (how many?), 106,108,108,108,109.

105s: row1: 105 (4 times), row2:105 (1), row4:105 (1), row5:105 (2). Total 4+1+1+2=8. 106:1, 108:3 (row1:108, row3:108,108), 109:1. So 8+1+3+1=13? Wait 8+1=9, +3=12, +1=13.

110-114:111,114,114 (row3:114, row5:114), 111 (row3:111). Wait row3:111,114; row5:114. Also row4:119? No, 110-114: 111,114,114, and any others? Wait row2:115 (no, 115 is 115-119). Row3:111,114; row4:118 (no), row5:114. Wait also row2:115 is 115-119. Wait 110-114: 111,114,114, and is there 110? No. Wait data points: 111,114,114, and any others? Wait row3:111,114; row5:114. Also row4:119? No. Wait maybe 111,114,114, and is there 112,113? No. Wait count: 111 (1), 114 (2) → total 3? Wait no, let's list all 110-114:

Looking at all data:

111 (row3), 114 (row3), 114 (row5), and any others? Wait row2:115 (no), row4:118 (no), row5:114 (yes). Wait also row2:119 (no), row4:119 (no). Wait maybe I missed: row3:114, row5:114, row3:111, and is there 110? No. Wait maybe 111,114,114, and another 114? Wait row5:114 is one, row3:114 is one. Wait maybe 3? No, wait original data:

Row3: 104,95,111,108,108,99,94,98,103,114 → 111,114

Row4: 87,89,102,100,119,119,109,101,118,105 → no 110-114

Row5: 104,105,94,93,87,114,99,116,116,105 → 114

Wait also row2: 93,89,100,98,97,119,105,106,115,95 → 115 (115-119)

Row1: 108,105,89,105,105,105,91,100,86,89 → no 110-114

Wait maybe I made a mistake. Let's count again:

110-114: 111 (1), 114 (2) → total 3? No, wait row3 has 114, row5 has 114, and is there another 114? Wait row5: 114 is one, row3:114 is one. Wait maybe 2? No, row3:114, row5:114, and row3:111. So 111,114,114 → 3?

115-119:115,116,116,118,119,119,119? Wait row2:115,119; row3:114 (no), row4:118,119,119; row5:116,116. So 115 (1), 116 (2), 118 (1), 119 (3). Total 1+2+1+3=7.

Wait let's check total frequency: 7+5+7+8+13+3+7= 7+5=12, +7=19, +8=27, +13=40, +3=43, +7=50. Perfect, total 50.

So correct frequencies:

• 85 - 89: 7
• 90 - 94: 5
• 95 - 99: 7
• 100 - 104: 8
• 105 - 109: 13
• 110 - 114: 3
• 115 - 119: 7

Answer:

Class	Frequency
90 - 94	5
95 - 99	7
100 - 104	8
105 - 109	13
110 - 114	3
115 - 119	7