Cumulative Frequency and Mean Calculations

The video tutorial covers the analysis of a cumulative frequency histogram to find the frequency of a group with a class center of 75 km/h. It explains how to construct a cumulative frequency polygon and use it to estimate the median speed. The tutorial also demonstrates calculating the mean weight of a group of students when an additional data point is added, emphasizing the importance of clear working and structured solutions.

What is the first step in determining the frequency of a group with a class center of 75 km/h from a cumulative frequency histogram?

• Add the frequencies of all groups

• Identify the cumulative frequency at 75 km/h

• Subtract the cumulative frequency at 75 km/h from the total

• Multiply the class center by the total frequency

What is the purpose of constructing a cumulative frequency polygon?

• To calculate the total number of data points

• To visualize the distribution of frequencies

• To find the mean of the data set

• To determine the range of the data set

When constructing a cumulative frequency polygon, what is the correct way to draw the lines?

• From the top left to the bottom right

• From the bottom left to the top right

• From the top right to the bottom left

• From the center to the edges

How do you determine the median speed using a cumulative frequency polygon?

• Find the midpoint of the horizontal axis

• Locate the median position on the vertical axis and draw a line to the polygon

• Calculate the average of all speeds

• Subtract the lowest speed from the highest speed

What is a common mistake when estimating the median from a cumulative frequency graph?

• Ignoring the class intervals

• Calculating the mean instead of the median

• Assuming the total frequency is the highest point on the vertical axis

• Using the wrong scale on the horizontal axis

In the mean weight problem, what does the increase of 1.03 kg represent?

• The difference between the heaviest and lightest student

• The increase in the mean weight of the group

• The total weight of the group

• The weight of the 15th student

What is the formula for calculating the mean of a group?

• Product of the number of people and the mean weight

• Difference between the highest and lowest weight

• Sum of all weights

• Total weight divided by the number of people

How do you find the total weight of the original group of 14 students?

• Add the weights of all students

• Multiply the mean weight by the number of students

• Subtract the mean weight from the total weight

• Divide the total weight by the number of students

What is the final step in calculating the weight of the 15th student?

• Divide the total weight by 15

• Add the total weights of both groups

• Subtract the total weight of the original group from the new group

• Multiply the mean weight by 15

Why is it important to clearly label calculations when solving problems?

• To ensure clarity and understanding of each step

• To make the solution look longer

• To confuse the examiner

• To avoid using a calculator