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Question
The mean height of 11 students in a group is 150 cm. The heights of the students are 154 cm, 145 cm, Y cm, Y + 4 cm, 160 cm, 151 cm, 149 cm, 149 cm, 150 cm, 144 cm and 140 cm. Find the value of Y and the heights of two students?
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Solution
Mean Height = `"Sum of heights of all students"/"Number of students"`
150 = `(154 + 145 + "Y" + ("Y" + 4) + 160 + 151 + 149 + 149 + 150 + 144 + 140)/11`
150 = `(1342 + "Y" + "Y" + 4)/11`
150 = `(1346 + 2"Y")/11`
150 × 11 = 1346 + 2Y
1650 = 1346 + 2Y
2Y = 1650 – 1346 = 304
Y = `304/2` = 152
Height of two students are Y and Y + 4
⇒ 152 and 152 + 4
⇒ 152 cm and 156 cm
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