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All questions of Averages for Year 6 Exam

What is the mean of the following heights: 138 cm, 140 cm, 136 cm, 141 cm, 142 cm, 137 cm?
  • a)
    140 cm
  • b)
    138 cm
  • c)
    141 cm
  • d)
    139 cm
Correct answer is option 'D'. Can you explain this answer?

Subset Academy answered
The mean is calculated by summing all values and dividing by the number of values: (138 + 140 + 136 + 141 + 142 + 137) = 834, then 834 ÷ 6 = 139 cm. The mean provides an overall average, which can summarize data effectively for comparison.
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If the mean of a dataset is significantly lower than the median, what might this suggest?
  • a)
    There are extreme low values present
  • b)
    The dataset is bimodal
  • c)
    The median is incorrectly calculated
  • d)
    The dataset is uniform
Correct answer is option 'A'. Can you explain this answer?

Subset Academy answered
A mean that is significantly lower than the median often suggests the presence of extreme low values (outliers) that pull the average down. This situation highlights the importance of examining both mean and median for a complete understanding of data distribution.

Why might the mean not accurately represent a dataset with extreme outliers?
  • a)
    It is too complicated to calculate
  • b)
    The mean is not a valid measure
  • c)
    It always gives a higher value than the median
  • d)
    Extreme values can skew the average significantly
Correct answer is option 'D'. Can you explain this answer?

Edgy Education answered
The mean can be significantly skewed by extreme outliers, leading to a representation that may not reflect the typical values in the dataset. This is why it is often important to consider other measures, such as the median, especially in skewed distributions.

How would one describe a dataset with a large range?
  • a)
    It has high consistency
  • b)
    It has little variability
  • c)
    It is composed of mostly identical values
  • d)
    It shows a wide spread of values
Correct answer is option 'D'. Can you explain this answer?

Edgy Education answered
A large range indicates a wide spread of values within the dataset, suggesting significant variability. This can be important in fields such as education or sports, where understanding differences can inform strategies for improvement.

When comparing two datasets, which measure would be most useful to determine consistency?
  • a)
    Mode
  • b)
    Mean
  • c)
    Range
  • d)
    Median
Correct answer is option 'C'. Can you explain this answer?

Torcia Education answered
The range is a valuable measure when comparing consistency between two datasets. A smaller range in one dataset suggests that the values are more consistent, while a larger range indicates greater variability, which can be critical for performance assessments.

If the average score of a test is 60%, what can be inferred?
  • a)
    All students scored below 60%
  • b)
    More students scored above 60% than below
  • c)
    The typical performance of students is around 60%
  • d)
    The test was too difficult for all students
Correct answer is option 'C'. Can you explain this answer?

Freak Artworks answered
An average score of 60% indicates that the typical performance of students is around that value. It gives a general impression of how well the class performed collectively, although individual scores may vary widely.

For the heights 127 cm, 137 cm, 152 cm, 129 cm, 135 cm, 136 cm, and 141 cm, what is the range?
  • a)
    20 cm
  • b)
    25 cm
  • c)
    30 cm
  • d)
    15 cm
Correct answer is option 'B'. Can you explain this answer?

Subset Academy answered
The range is calculated as the highest value (152 cm) minus the lowest value (127 cm), resulting in a range of 152 - 127 = 25 cm. This measure of spread can help identify how consistent or variable a dataset is.

What does the range of a dataset indicate?
  • a)
    The difference between the highest and lowest values
  • b)
    The most frequently occurring value
  • c)
    The average of the values
  • d)
    The total number of values
Correct answer is option 'A'. Can you explain this answer?

Subset Academy answered
The range is the difference between the highest and lowest values in a dataset, providing insight into the spread of the data. For example, a larger range may suggest greater variability within the dataset, which can be crucial for understanding data distributions.

Why might a researcher choose to use the median instead of the mean?
  • a)
    The median is less affected by outliers
  • b)
    The median applies only to even datasets
  • c)
    The median is easier to calculate
  • d)
    The median is always higher than the mean
Correct answer is option 'A'. Can you explain this answer?

Subset Academy answered
The median is less affected by outliers and extreme values, making it a more reliable measure of central tendency in skewed distributions. For example, in income data, a few very high incomes can skew the mean, but the median remains stable.

Which of the following is true about the mean?
  • a)
    It is always greater than the median
  • b)
    It is less informative than the mode
  • c)
    It is the sum of values divided by the number of values
  • d)
    It can be calculated using categorical data
Correct answer is option 'C'. Can you explain this answer?

Rahul Kumar answered
The mean is calculated by summing all values and dividing by the total number of values. This statistic provides a useful overall average but can be influenced by extreme values, unlike the median.

If the heights of a group of children are 138 cm, 140 cm, 136 cm, 141 cm, 142 cm, and 137 cm, what is the median height?
  • a)
    140 cm
  • b)
    141 cm
  • c)
    139 cm
  • d)
    138 cm
Correct answer is option 'C'. Can you explain this answer?

Torcia Education answered
To find the median, first arrange the heights: 136 cm, 137 cm, 138 cm, 140 cm, 141 cm, 142 cm. With six values (even), the median is the average of the third and fourth values: (138 + 140) ÷ 2 = 139 cm. The median provides a more reliable central tendency than the mean when data is skewed.

In which scenario would using the mode be the most appropriate measure of central tendency?
  • a)
    Assessing average temperature
  • b)
    Analyzing test scores
  • c)
    Determining the most popular product
  • d)
    Calculating average height
Correct answer is option 'C'. Can you explain this answer?

Rahul Kumar answered
The mode is particularly useful for identifying the most popular item in a dataset, such as the most commonly sold product. It highlights what is most frequently chosen or preferred, which is often more informative in categorical data.

What does a dataset with a mode of 0 indicate?
  • a)
    The data is bimodal
  • b)
    Zero is the most frequently occurring value
  • c)
    All values are positive
  • d)
    The dataset has no values
Correct answer is option 'B'. Can you explain this answer?

Subset Academy answered
A mode of 0 indicates that zero is the most frequently occurring value in the dataset. This can be significant in various contexts, such as economic data where zero might represent no sales or no activity occurring.

In a classroom assessment, if the scores are 5, 7, 8, 6, 6, and 9, what is the mode of the scores?
  • a)
    8
  • b)
    6
  • c)
    7
  • d)
    5
Correct answer is option 'B'. Can you explain this answer?

Subset Academy answered
The mode is the value that appears most frequently in a dataset. In this case, the score of 6 appears twice, more than any other score, making it the mode. This information can help teachers identify which scores are most common among students.

If the average height of a group of adults is found to be 175 cm, what does this mean?
  • a)
    All adults are exactly 175 cm tall
  • b)
    The majority of adults are taller than 175 cm
  • c)
    There are no adults shorter than 175 cm
  • d)
    The average height is representative of the group
Correct answer is option 'D'. Can you explain this answer?

Torcia Education answered
An average height of 175 cm suggests that this value is representative of the group, summarizing the heights of all individuals. It provides a useful benchmark for understanding the typical height within that population, though individual heights may vary.

If a dataset is bimodal, what does that imply?
  • a)
    All values are unique
  • b)
    There is no mode
  • c)
    There is one value that occurs most frequently
  • d)
    There are two values that occur with the highest frequency
Correct answer is option 'D'. Can you explain this answer?

Keystone Instructors answered
A bimodal dataset has two values that appear with the same highest frequency. This characteristic can indicate that there are two prevalent groups or categories within the data, which can be significant in analysis.

What is the importance of selecting the appropriate average (mode, median, or mean) in data analysis?
  • a)
    It enhances clarity and accuracy in interpretation
  • b)
    It allows for easier calculations
  • c)
    It eliminates the need for data collection
  • d)
    It always gives the same result
Correct answer is option 'A'. Can you explain this answer?

Keystone Instructors answered
Choosing the appropriate average is crucial for enhancing clarity and accuracy in data interpretation. Different measures provide different insights; for instance, the mode highlights frequency, while the mean gives an overall average. Selecting the right one depends on the data context and the specific analysis goals.

How is the median calculated when there is an even number of data points?
  • a)
    By counting the total number of values
  • b)
    By averaging the two middle values
  • c)
    By choosing the lowest value
  • d)
    By selecting the highest value
Correct answer is option 'B'. Can you explain this answer?

Rahul Kumar answered
When there is an even number of data points, the median is found by arranging the data in ascending order and averaging the two middle values. This method helps provide a central value that is less affected by extreme values compared to the mean.

An average score of 7/10 indicates what about the typical reader's opinion?
  • a)
    Most readers did not like the book
  • b)
    Readers found the book satisfactory
  • c)
    The book was universally praised
  • d)
    The book was rated lower than expected
Correct answer is option 'B'. Can you explain this answer?

Freak Artworks answered
An average score of 7/10 suggests that readers generally found the book satisfactory, as it indicates a positive reception without being overwhelmingly high. This average score can help authors and publishers gauge the success of their work.

What is the mode of the following dataset: 5, 2, 4, 2, 3, 2, 1, 2, 5, 4, 5?
  • a)
    2
  • b)
    5
  • c)
    4
  • d)
    3
Correct answer is option 'A'. Can you explain this answer?

Subset Academy answered
The mode is defined as the most frequently occurring value in a dataset. In this case, the number 2 appears four times, more than any other number, making it the mode. Understanding the mode helps identify the most common items in various contexts, such as customer preferences.

Chapter doubts & questions for Averages - Year 6 Mathematics IGCSE (Cambridge) 2025 is part of Year 6 exam preparation. The chapters have been prepared according to the Year 6 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Year 6 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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