The problem provides a cumulative frequency distribution table and asks us to complete it, draw a cumulative frequency curve, and find the median. Then, it asks us to find the difference between the median and the midpoint of the median class interval.

1. Problem Description

The problem provides a cumulative frequency distribution table and asks us to complete it, draw a cumulative frequency curve, and find the median. Then, it asks us to find the difference between the median and the midpoint of the median class interval.

2. Solution Steps

(i) Completing the table:

The cumulative frequency for the 40-50 class is $26 + 15 = 41$.

The cumulative frequency for the 50-60 class is $48$. So, the frequency is $48 - 41 = 7$.

The cumulative frequency for the 60-70 class is $48$. So, $41+7 = 48$. The frequency of the 60-70 class is therefore

0.

Completed Table:

| Class Interval | Frequency | Cumulative Frequency |

|---|---|---|

| 10-20 | 6 | 6 |

| 20-30 | 8 | 14 |

| 30-40 | 12 | 26 |

| 40-50 | 15 | 41 |

| 50-60 | 7 | 48 |

| 60-70 | 0 | 48 |

(ii) Drawing the cumulative frequency curve and finding the median:

We need to plot the cumulative frequencies against the upper class boundaries. The points to plot are:

(20, 6), (30, 14), (40, 26), (50, 41), (60, 48), (70, 48).

The total frequency is 48, so the median corresponds to the 24th value.

Since a graph is required, we cannot provide an exact calculation. From the completed table, we can see that the median lies between the 30-40 class interval. Approximating based on the table the value looks to be around

3

9. We will proceed with an estimate median value of

3

9.

(iii) Finding the difference between the median and the midpoint of the median class interval:

The median class interval is 30-

4

0. The midpoint of the median class interval is $(30+40)/2 = 35$.

The estimated median is approximately

3

9. The difference between the median and the midpoint of the median class is $39 - 35 = 4$.

3. Final Answer

(i) Completed table is shown above.

(ii) The median value is approximately 39, based on a roughly sketched cumulative frequency distribution based on the table above.

(iii) The difference between the median and the midpoint of the median class interval is

4.