Solving Statistics Problems On Frequency Distribution table

 

Frequency Distribution Table Quiz

Section 1: Basic Reading and Interpretation

Scenario: A local library tracked the number of books read by 30 students during a school break. The data is organized in the frequency table below:

Books Read	Number of Students (Frequency)
0 – 2	5
3 – 5	12
6 – 8	8
9 – 11	4
12 – 14	1

1. What is the class width (size) of each interval in this table?

• A) 2
• B) 3
• C) 4
• D) 5

Solution: Count the integers included in the range (e.g., 0, 1, 2 gives a total width of 3).

2. Which class interval is the modal class?

• A) 0 – 2
• B) 3 – 5
• C) 6 – 8
• D) 12 – 14

Solution: The modal class has the highest frequency. The interval 3 – 5 has the highest frequency (12).

3. How many students read 6 or more books?

• A) 8
• B) 12
• C) 13
• D) 25

Solution: Add frequencies for 6–8, 9–11, and 12–14 intervals: 8 + 4 + 1 = 13.

4. What percentage of the total students read between 3 and 5 books?

• A) 12%
• B) 30%
• C) 40%
• D) 50%

Solution: (12 students / 30 total) * 100 = 40%.

Section 2: Calculations and Mean from Grouped Data

Scenario: The table below shows the daily high temperatures (in °C) recorded over a 20-day period.

Temperature Range (°C)	Frequency (f)
20 – 24	3
25 – 29	7
30 – 34	8
35 – 39	2

5. What is the midpoint (x) for the 30 – 34 class interval?

• A) 31
• B) 32
• C) 33
• D) 34

Solution: Midpoint = (Lower limit + Upper limit) / 2 = (30 + 34) / 2 = 32.

6. Calculate the estimated mean temperature for this 20-day period.

• A) 27.5°C
• B) 29.25°C
• C) 30.0°C
• D) 31.5°C

Solution: Sum of (f * midpoints) = (3*22) + (7*27) + (8*32) + (2*37) = 66 + 189 + 256 + 74 = 585. Mean = 585 / 20 = 29.25°C.

7. What is the cumulative frequency up to the 30 – 34 temperature range?

• A) 8
• B) 10
• C) 18
• D) 20

Solution: Add the frequencies up to that class: 3 + 7 + 8 = 18.

Section 3: Cumulative Frequency & Advanced Concepts

Scenario: An electronics store recorded the lifetimes (in hundreds of hours) of 50 electronic components.

Lifetime (Hundreds of Hours)	Frequency	Cumulative Frequency
0 – 9	4	4
10 – 19	11	15
20 – 29	18	33
30 – 39	12	45
40 – 49	5	50

8. What are the exact class boundaries for the interval 10 – 19?

• A) 10.0 – 19.0
• B) 9.5 – 19.5
• C) 10.5 – 19.5
• D) 9.5 – 20.5

Solution: Subtract 0.5 from the lower limit and add 0.5 to the upper limit to bridge the data gaps: 9.5 – 19.5.

9. In which class interval does the median value lie?

• A) 10 – 19
• B) 20 – 29
• C) 30 – 39
• D) 40 – 49

Solution: Median index position is 50 / 2 = 25. Looking at cumulative frequency, the 25th position lands inside the 20 – 29 group (which spans from items 16 to 33).

10. If a component is selected at random, what is the probability that its lifetime is less than 30 (hundred hours)?

• A) 15/50
• B) 18/50
• C) 33/50
• D) 45/50

Solution: "Less than 30" includes intervals 0-9, 10-19, and 20-29. Their combined cumulative frequency total is 33. Probability = 33 / 50.

Quiz Complete!