Solving Problems On Mode Median And Mean

 

Grade 10 Math: Data Management Quiz
Measures of Central Tendency & Spread

1. A student records their math quiz scores out of 10: 6, 8, 7, 9, 8, 10, 6, 8. What is the mode of these scores?

• A) 6
• B) 8
• C) 7.75
• D) 4

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Formula: Mode = The value that occurs most frequently

Brief Solution: Count the frequency of each number. 6 appears twice, 7 appears once, 8 appears three times, 9 appears once, and 10 appears once.

Correct Answer: B (8)

2. Find the median of the following set of daily high temperatures (in Celsius): -3, 2, -1, 5, 0, 4, -2.

• A) -1 °C
• B) 0.71 °C
• C) 0 °C
• D) 5 °C

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Formula: Median = The middle value when data is arranged in order

Brief Solution: 1. Arrange the data from least to greatest: -3, -2, -1, 0, 2, 4, 5.
2. Locate the middle position. Since there are 7 data points (an odd number), the 4th position is the exact middle.

Correct Answer: C (0 °C)

3. Consider the following table showing the number of goals scored by a hockey team over 6 games:

Game	Goals Scored
1	2
2	5
3	1
4	4
5	3
6	3

• A) 3.0
• B) 3.5
• C) 4.0
• D) 18.0

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Formula: Mean = (Sum of all values) ÷ (Total number of data points)

Brief Solution:
1. Sum = 2 + 5 + 1 + 4 + 3 + 3 = 18
2. Total games (n) = 6
3. Mean = 18 ÷ 6 = 3.0

Correct Answer: A (3.0)

4. The range of a set of data is 24. If the lowest value (minimum) in the dataset is 11, what is the highest value (maximum)?

• A) 13
• B) 24
• C) 35
• D) 46

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Formula: Range = Maximum value - Minimum value

Brief Solution: Rearrange the formula to solve for the Maximum:
Maximum = Range + Minimum
Maximum = 24 + 11 = 35

Correct Answer: C (35)

5. A local coffee shop tracks the number of espresso shots added to specialty drinks over an hour:

Shots Added (x)	Frequency (f)
1	5
2	12
3	4
4	2

• A) 2
• B) 12
• C) 2.13
• D) 3

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Formula: Mode = The data value with the highest frequency

Brief Solution: Look down the "Frequency" column to find the highest number, which is 12. The corresponding data value in the "Shots Added" column is 2.

Correct Answer: A (2)

6. An even number of data points are already arranged in order: 12, 15, 17, 21, 25, 30. How do you calculate the median?

• A) Take the difference between 30 and 12.
• B) Select 17 because it is on the left side of the middle.
• C) Add all values and divide by 6.
• D) Find the mean of 17 and 21.

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Formula: Median (for even n) = (Sum of the two middle values) ÷ 2

Brief Solution: There are 6 items. The two middle values are the 3rd and 4th terms, which are 17 and 21. You must average them: (17 + 21) ÷ 2 = 19.

Correct Answer: D (Find the mean of 17 and 21.)

7. A small retail business has five employees who earn hourly wages of $16, $16, $18, $20, and $45. Which measure of central tendency is distorted the most by the $45 outlier?

• A) Mode
• B) Median
• C) Mean
• D) Range

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Concept: The Mean is sensitive to outliers because it incorporates every exact value.

Brief Solution:
- Without $45, the mean is $17.50. With $45, it jumps to $23.00 (higher than what 4 out of 5 people make).
- The median remains $18 and the mode remains $16 regardless of the outlier value.

Correct Answer: C (Mean)

8. A teacher organizes the class project percentages into a frequency table:

Mark (%)	Number of Students (f)
65	3
75	7
85	8
95	2

• A) 4
• B) 20
• C) 30
• D) 80

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Formula: n = Σf (Sum of all frequencies)

Brief Solution: Add up the number of students in each category to find the total sample size: 3 + 7 + 8 + 2 = 20.

Correct Answer: B (20)

9. A set of four numbers has a mean of 10. If three of the numbers are 8, 11, and 12, what is the fourth number?

• A) 7
• B) 9
• C) 10
• D) 11

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Formula: Required Total Sum = Mean × n

Brief Solution:
1. Calculate required total sum: 10 × 4 = 40
2. Sum the known numbers: 8 + 11 + 12 = 31
3. Subtract to find the missing number: 40 - 31 = 9.

Correct Answer: B (9)

10. You are given the dataset: 5, 5, 7, 8, 10. If a new number, 15, is added to this dataset, which of the following statements is true?

• A) The mode changes.
• B) The mean decreases.
• C) The range increases.
• D) The median changes to 8.5.

Click for Solution

Formula: Range = Maximum - Minimum

Brief Solution:
- Original Range: 10 - 5 = 5
- New Range (with 15 included): 15 - 5 = 10.
Since the new value is higher than the previous maximum, the gap between the largest and smallest numbers expands.

Correct Answer: C (The range increases.)