Question 5
Convert the given frequency distribution into a continuous grouped frequency distribution.
Class intervalFrequency150−1537154−1577158−16115162−16510166−1695170−1736
In which intervals would 153.5 and 157.5 be included?
Question 5
Convert the given frequency distribution into a continuous grouped frequency distribution.
Class intervalFrequency150−1537154−1577158−16115162−16510166−1695170−1736
In which intervals would 153.5 and 157.5 be included?
It is clear that the given table is in inclusive (discontinuous) form. So, we first convert it into exclusive form.
Now, consider the classes 150 - 153, 154 - 157.
∴ Lower limit of 154 - 157 = 154
And upper limit of 150 - 153 = 153
Required difference = 154 - 153 = 1
So, half the difference
=12=0.5
So, we subtract 0.5 from each lower limit and add 0.5 to each upper limit. The table for continuous grouped frequency distribution is given below.
Class intervalFrequency149.5−153.57153.5−157.57157.5−161.515161.5−165.510165.5−169.55169.5−173.56
Thus, 153.5 and 157.5 included in class intervals 153.5 - 157.5 and 157.5 – 161.5 respectively.
It is clear that the given table is in inclusive (discontinuous) form. So, we first convert it into exclusive form.
Now, consider the classes 150 - 153, 154 - 157.
∴ Lower limit of 154 - 157 = 154
And upper limit of 150 - 153 = 153
Required difference = 154 - 153 = 1
So, half the difference
=12=0.5
So, we subtract 0.5 from each lower limit and add 0.5 to each upper limit. The table for continuous grouped frequency distribution is given below.
Class intervalFrequency149.5−153.57153.5−157.57157.5−161.515161.5−165.510165.5−169.55169.5−173.56
Thus, 153.5 and 157.5 included in class intervals 153.5 - 157.5 and 157.5 – 161.5 respectively.
