Question 6 - Figure it out - Page 113-116 - Chapter 5 Class 8 - Tales by Dots and Lines (Ganita Prakash II)

Transcript

Question 6 Examine the statements below and justify if the statement is always true, sometimes true, or never true. (i) Removing a value less than the median will decrease the median.Removing a smaller value shifts the middle position to the right, which will either increase the median or keep it the same. Thus, this statement is Never True Example: If our numbers are 8, 9, 10, 11, 12 Median = 10 If we remove 8, Our numbers become 9, 10, 11, 12 Median = (10 + 11)/2 = 10.5 Thus, Median increased So, the statement is never true Question 6 Examine the statements below and justify if the statement is always true, sometimes true, or never true. (ii) Including a value less than the mean will decrease the mean.Adding a value below the average will continually pull the overall average down. Thus, this statement is Always true. Example: If our numbers are 8, 9, 10 Mean = (8+9+10)/3 = 27/3 = 9 If we add a smaller number, like 7, Our numbers become 7, 8, 9, 10 Mean = (7+8+9+10)/4 = 34/4 = 8.5 Thus, mean decreases Question 6 Examine the statements below and justify if the statement is always true, sometimes true, or never true. (iii) Including any 4 values will not affect the median.If you intentionally add two numbers above the median and two numbers below it, the median won't change. However, if you add four massive numbers, the median will increase. Thus, this statement is Sometimes true Question 6 Examine the statements below and justify if the statement is always true, sometimes true, or never true. (iv) Including 4 values less than the median will increase the median.Adding smaller values pulls the center position to the left, which will only ever decrease the median or keep it the same. Thus, this statement is Never true