To find the missing number, first calculate the total sum of all five numbers by multiplying the average of 20 by the count of 5, which equals 100. Next, add the four known values (10, 15, 25, and 30) to get a partial sum of 80. Finally, subtract this partial sum from the total sum of 100, revealing that the fifth number must be 20. This process demonstrates how the definition of an average allows us to reconstruct missing data points using simple arithmetic.

Question 2 Medium Mcq

✓ Correct ✗ Incorrect

If the average speed of a car is 60 miles per hour for the first half of the journey and 40 miles per hour for the second half, what is the overall average speed?

60 miles per hour

40 miles per hour

50 miles per hour

Cannot be determined without additional information

Explanation:

The overall average speed is not a simple arithmetic mean of the two speeds because the car spends equal time traveling at each speed only if the distances were different, but here the distances are equal. Since average speed equals total distance divided by total time, we must calculate the time taken for each half of the journey. The slower speed of 40 mph dominates the total time, pulling the average below the arithmetic mean of 50 mph. The correct calculation involves summing the distances and dividing by the sum of the times for each segment. This results in the harmonic mean of the two speeds, which accurately reflects the overall rate for the entire trip. Therefore, the overall average speed is indeed 48 mph, making the option closest to this value the correct choice in this context.

Question 3 Easy Mcq

✓ Correct ✗ Incorrect

A soccer team scored 2 goals in the first game, 4 goals in the second game, and 1 goal in the third game. What is the average number of goals scored per game?

2 goals

4 goals

1 goal

2.33 goals

Explanation:

To find the average, first sum the total goals scored across all three games, which equals 2 plus 4 plus 1 for a total of 7 goals. Next, divide this total sum by the number of games played, which is 3. Performing the division of 7 by 3 results in approximately 2.33, confirming that the average number of goals per game is 2.33. This calculation demonstrates how the mean represents the central value derived from the total quantity distributed evenly over the specific count of events.

Question 4 Easy Mcq

✓ Correct ✗ Incorrect

What is the average of the numbers 10, 15, and 20?

Explanation:

To find the average, you sum the given numbers 10, 15, and 20 to get a total of 45. You then divide this sum by the count of the numbers, which is 3. Dividing 45 by 3 results in exactly 15, demonstrating that the average represents the central value derived from equal distribution. This calculation confirms that 15 is the correct result for this specific set of data. Understanding this process helps verify that the middle number in a simple arithmetic progression often matches the mean.

Question 5 Easy Mcq

✓ Correct ✗ Incorrect

A store sold 100 items, with 50 items priced at $10 each and the remaining 50 items priced at $20 each. What is the average price of the items?

$10

$20

$15

$30

Explanation:

To find the average price, we first calculate the total revenue by multiplying the quantity of each item by its price, resulting in $500 for the first group and $1,000 for the second. Adding these amounts gives a total value of $1,500 for all 100 items sold. Dividing this total sum by the total number of items yields an average price of $15 per item. This demonstrates that the mean is simply the total value distributed equally across every single unit.

Question 6 Easy Mcq

✓ Correct ✗ Incorrect

A car traveled 200 miles on Monday, 250 miles on Tuesday, and 150 miles on Wednesday. What is the average distance traveled per day?

200 miles

250 miles

150 miles

200 miles

Explanation:

To find the average distance, first sum the daily distances of 200, 250, and 150 miles to get a total of 600 miles. Next, divide this total by the number of days, which is three, resulting in an average of 200 miles per day. This calculation demonstrates that the average represents the equal daily distance if the car had traveled the same amount every day. The result matches the first option provided in the list. Therefore, 200 miles is the correct value for the average distance traveled.

Question 7 Easy Mcq

✓ Correct ✗ Incorrect

If the average age of a family of four members is 30 years, what is the sum of their ages?

30 years

60 years

90 years

120 years

Explanation:

The average age represents the total sum of ages divided by the number of family members. To find the total sum, simply multiply the average age of 30 years by the four members in the family. This calculation yields 120 years, which accurately reflects the combined age of all individuals. Understanding this relationship between average, count, and sum is fundamental to solving such problems.

Question 8 Easy Mcq

✓ Correct ✗ Incorrect

A student scored 80, 90, and 85 on three exams. What is their average score?

Explanation:

To find the average, sum the three exam scores of 80, 90, and 85 to get a total of 255, then divide this sum by the number of exams, which is three. Performing the division of 255 by 3 yields exactly 85, confirming that this value represents the central tendency of the student's performance across all tests.

Question 9 Easy Mcq

✓ Correct ✗ Incorrect

The average temperature on Monday was 20 degrees Celsius, and on Tuesday it was 25 degrees Celsius. What was the average temperature over the two days?

20 degrees Celsius

25 degrees Celsius

22.5 degrees Celsius

45 degrees Celsius

Explanation:

To find the average temperature over two days, you sum the individual daily temperatures and divide by the number of days. Adding Monday's 20 degrees and Tuesday's 25 degrees gives a total of 45 degrees. Dividing this sum by the two days results in 22.5 degrees Celsius, which represents the central value of the dataset. This calculation correctly applies the arithmetic mean formula to determine the overall average.

Question 10 Easy Mcq

✓ Correct ✗ Incorrect

In a class of 20 students, the average height is 150 cm. If a new student joins the class with a height of 160 cm, what happens to the average height?

It stays the same, 150 cm

It increases

It decreases

Cannot be determined without additional information

Explanation:

When a student taller than the current average joins the group, the sum of all heights increases by a larger amount than the number of students. Since the new average is calculated by dividing this larger total height by the increased number of students, the resulting value must be higher than the original average. This mathematical principle ensures that adding a value greater than the mean always pulls the mean upward, causing the average height to increase.

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