There were 2 new admissions to Sudhakar's class just a couple of days after the class average height was found to be 150.2 cm. (i) Which of the following statements are correct? Why? (a) The average height of the class will increase as there are 2 new values. (b) The average height of the class will remain the same. (c) The heights of the new students have to be measured to find out the new average height. (d) The heights of everyone in the class has to be measured again to calculate the new average height. (ii) The heights of the two new joinees are 149 cm and 152 cm. Which of the following statements about the class' average height are correct? Why? (a) The average will remain the same. (b) The average will increase. (c) The average will decrease. (d) The information is not sufficient to make a claim about the average. (iii) Which of the following statements about the new class average height are correct? Why? (a) The median will remain the same. (b) The median will increase. (c) The median will decrease. (d) The information is not sufficient to make a claim about median.
Statement (c) is correct: The heights of the new students must be known to calculate the new average. Statement (d) is incorrect: We don't need to remeasure everyone; we can use the previous average and the new heights.
Statement (b) is correct: The average will increase. The average of the two new heights is (149 + 152)/2 = 150.5 cm, which is greater than the current average of 150.2 cm. Adding values with an average higher than the current mean will increase the overall average.
Statement (d) is correct: The information is not sufficient to make a claim about the median. Without knowing the distribution of all heights and where the new values (149 cm and 152 cm) fall in the sorted order, we cannot determine how the median changes.
Explanation
(i) The chapter shows that to find a new mean when values are added, we need to know those values but don't need to remeasure existing data. (ii) When values are added whose average exceeds the current mean, the new mean increases. (iii) The median depends on the position of values in sorted data. Without knowing the full distribution, we cannot predict the median's change.