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Averages from Grouped Frequency Table

Probability and Statistics Averages from Grouped Frequency Table

Courses Overview

🎬 Video Tutorial

(0:01) What is A Grouped Frequency Table?: A grouped frequency table organises data into intervals, making it easier to handle large datasets.
(0:50) What is the Modal Class?: The modal class is the interval with the highest frequency.
(1:10) How to Find the Median Class?: Calculate the median position with $\large \frac{N + 1}{2}$, where $N$ is the total frequency. Then, locate this position in the cumulative frequencies.
(2:00) How to Calculate the Mean?: Find each interval’s midpoint, multiply by its frequency, and then sum these products. Divide by the total frequency to get the estimated mean.

📂 Revision Cards

Grouped frequency table showing delivery time intervals in minutes and their corresponding frequencies. — 1) Grouped Frequency Table

Delivery time grouped frequency table highlighting the modal class as x is greater than forty and less than or equal to fifty with the highest frequency of 10. — 2) Modal Class

Grouped frequency table for delivery times, showing frequencies and positions to identify the class containing the median. — 3) Median from a Grouped Frequency Table

Grouped frequency table showing delivery times in minutes, with corresponding frequencies, mid-points, and frequency multiplied by mid-points. — 4) Mean from a Grouped Frequency Table

Grouped frequency table showing delivery time intervals and frequencies, with explanations of the modal class, class with the median, estimated mean. — 5) Summary

🍪 Quiz Time - Practice Now!

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Averages from Grouped Frequency Table

1 / 6

Q: The table shows the ages of people attending a concert. How many people are represented in total?

20

15

25

18

Feedback: Not quite! Add all the frequencies: 6 + 8 + 4 + 2 = 20 people attended the concert.

Feedback: Well done! Add all the frequencies: 6 + 8 + 4 + 2 = 20 people attended the concert.

2 / 6

Q: The table shows the ages of people attending a concert. What is the modal class for the data?

30–40 years

20–30 years

40–50 years

10–20 years

Feedback: Not quite! The modal class is the age group with the highest frequency. Here, 20–30 years has the highest frequency of 8 people.

Feedback: Well done! The modal class is the age group with the highest frequency. Here, 20–30 years has the highest frequency of 8 people.

3 / 6

Q: The table below shows the delivery times for a courier service. Which class contains the median delivery time?

10–20 minutes

20–30 minutes

30–40 minutes

40–50 minutes

Feedback: Not quite! First, find the total frequency: 4 + 7 + 6 + 3 = 20 people. Since the total is even, the median lies between the 10th and 11th values. The first 4 people fall in the 10–20 minute class, and the next 7 (5th to 11th) are in the 20–30 minute class. That means both the 10th and 11th values fall in the 20–30 minute class, so this class contains the median delivery time.

Feedback: Well done! First, find the total frequency: 4 + 7 + 6 + 3 = 20 people. Since the total is even, the median lies between the 10th and 11th values. The first 4 people fall in the 10–20 minute class, and the next 7 (5th to 11th) are in the 20–30 minute class. That means both the 10th and 11th values fall in the 20–30 minute class, so this class contains the median delivery time.

4 / 6

Q: What is the midpoint of the 20–30 minute interval?

25

20

30

22

Feedback: Not quite! The midpoint of the 20–30 minute interval is calculated as (20 + 30) ÷ 2 = 25.

Feedback: Well done! The midpoint of the 20–30 minute interval is calculated as (20 + 30) ÷ 2 = 25.

5 / 6

Q: If 2 more orders are added to the 30–40 minutes range, how will this affect the modal class?

The modal class will remain the same.

The modal class will change to 30–40 minutes.

The modal class will be 20–30 minutes and 30–40 minutes (tie).

There will be no modal class.

Feedback: Not quite! By adding 2 more orders to the 30–40 range, its frequency increases to 8, making it the highest frequency. The modal class becomes 30–40 minutes.

Feedback: Well done! By adding 2 more orders to the 30–40 range, its frequency increases to 8, making it the highest frequency. The modal class becomes 30–40 minutes.

6 / 6

Q: Using the table below, estimate the mean delivery time.

29 minutes

26 minutes

28 minutes

27 minutes

Feedback: Not quite! Multiply each midpoint by its frequency: (15 × 4) + (25 × 7) + (35 × 6) + (45 × 3) = 60 + 175 + 210 + 135 = 580. Then, divide by the total frequency: 580 ÷ 20 = 29 minutes.

Feedback: Well done! Multiply each midpoint by its frequency: (15 × 4) + (25 × 7) + (35 × 6) + (45 × 3) = 60 + 175 + 210 + 135 = 580. Then, divide by the total frequency: 580 ÷ 20 = 29 minutes.

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