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Quizzes > High School Quizzes > Mathematics

Central Tendency Practice Quiz: Choose the Correct Measure

Sharpen your central tendency skills with this quiz

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting a Mean, Median, Mode trivia quiz for middle school math students.

Which of the following is a measure of central tendency?
Range
Probability
Variance
Mean
Central tendency measures describe the central point of a data set. The mean, which is the arithmetic average, is one such key measure.
What is the median of the set [3, 1, 4]?
1
2
3
4
When the numbers are arranged in order, the median is the middle number. In the ordered set [1, 3, 4], the median is 3.
Which measure of central tendency is most affected by extreme values?
Median
Mean
Range
Mode
The mean takes into account all values and is highly sensitive to outliers and extreme values. The median and mode, however, remain relatively stable when extreme values are present.
What does the mode represent in a set of numbers?
Middle value
Average value
Difference between highest and lowest values
Most frequent value
The mode is defined as the value that occurs most frequently in a data set. It highlights which number appears most commonly among the data values.
The mean is calculated by adding all data values and dividing by which of the following?
The range
The number of data values
The largest value
The smallest value
To compute the mean, you sum all the numbers and then divide by the total count of the numbers. This process gives you the arithmetic average of the data set.
In the data set [5, 3, 9, 7, 3, 10], what is the mode?
5
7
3
10
The mode is the number that appears most frequently in the data set. In this case, the number 3 appears twice while the other numbers appear only once.
Find the mean of the numbers [4, 8, 12, 16].
8
12
10
14
To find the mean, add all the numbers and then divide by the number of values. Here, 4 + 8 + 12 + 16 equals 40, and dividing by 4 gives a mean of 10.
Given the set [2, 5, 7, 8, 10, 12], what is the median?
8.5
7
8
7.5
Since there is an even number of values, the median is calculated by averaging the two middle numbers. In this set, the middle numbers are 7 and 8, so the median is (7+8)/2 = 7.5.
Which measure of central tendency is most appropriate for a skewed distribution?
Mean
Median
Range
Mode
The median is less affected by extreme values and is therefore preferred when dealing with skewed distributions. It provides a more accurate representation of the center of such data sets.
What is the effect of an outlier on the mean?
It has no effect on the mean
It significantly affects the mean
It only affects the median
It doubles the mean
Outliers can heavily influence the mean because they alter the total sum of the data. In contrast, the median remains relatively stable even when outliers are present.
When all values in a dataset are unique, which measure of central tendency may offer little insight?
Mode
Mean
Median
Standard Deviation
The mode represents the most frequently occurring value. In a dataset where every value is unique, no number repeats, making the mode less useful.
Calculate the mean of the numbers [2, 3, 5, 7, 11, 13, 17].
7.00
9.00
8.00
8.29
First, add the numbers to get a total of 58. Dividing 58 by the 7 values in the dataset results in an approximate mean of 8.29.
Which statement accurately describes the median?
It is the most frequently occurring value
It is calculated by adding all values and dividing by the count
It is the middle value in an ordered set
It represents the difference between the highest and lowest values
The median is determined by arranging the data in order and selecting the middle value. This makes it less influenced by extreme values, unlike the mean.
In a dataset where a value at an extreme is removed, which measure of central tendency generally remains most stable?
Mean
Range
Mode
Median
The median is less affected by extreme values because it depends only on the middle value of the ordered list. Consequently, it remains more stable than the mean when an outlier is removed.
When faced with a bimodal distribution, which approach best represents the central tendency?
Determine the range
Use the median
Calculate only the mean
Report both modes
A bimodal distribution has two values that occur most frequently. Reporting both modes provides a comprehensive summary of the central tendencies present in the data.
A teacher recorded test scores: 72, 85, 90, 95, 100. If 90 was mistakenly entered instead of the correct score of 80, how does this error affect the mean?
It increases by 10
It increases by 2
It decreases by 2
It remains unchanged
Recording a score of 90 instead of 80 adds an extra 10 points to the total sum. Dividing this extra sum by the 5 scores increases the mean by 2.
In a normally distributed set of test scores, a data entry error changes an extreme high value from 150 to 15. Which measure of central tendency is most affected by this error?
Median
Mean
Mode
Range
The mean is highly sensitive to extreme values and outliers. A drastic reduction of a high value notably lowers the mean, while the median and mode remain relatively stable.
A set has a mean of 50 and a median of 48. After adding an outlier value of 100, which statement is most likely true?
Both increase equally
The median increases more than the mean
The mean increases more than the median
Both remain unchanged
An outlier, such as 100, significantly affects the mean because it contributes to the total sum, whereas the median largely depends on the middle value(s) and is less sensitive. Thus, the mean increases more than the median.
In an even-numbered data set, if the two middle numbers are 43 and 47, what is the median?
90
43
47
45
For an even-numbered data set, the median is calculated by taking the average of the two middle values. In this case, (43 + 47) / 2 equals 45.
A researcher analyzing data with outliers needs a measure of central tendency that is least influenced by extreme values. Which measure should they choose?
Range
Mode
Median
Mean
The median is known for its resistance to outliers, making it a more reliable indicator of central tendency when extreme values are present. Unlike the mean, the median is not skewed by unusually high or low values.
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Study Outcomes

  1. Identify the measures of central tendency including mean, median, and mode.
  2. Calculate the mean, median, and mode for a given dataset.
  3. Compare and contrast the different measures to understand their applications.
  4. Apply central tendency concepts to analyze real-world data examples.
  5. Evaluate the suitability of each measure when interpreting data variability.

Measures of Central Tendency Cheat Sheet

  1. Mean (Arithmetic Average) - Think of the mean as your friendly neighborhood average: add all the numbers and divide by how many there are to find the center. For example, the mean of 2, 4, 6, 8 and 10 is (2+4+6+8+10)/5 = 6. collegedunia.com
  2. Median (Middle Value) - The median is the middle number when your data is lined up from smallest to largest. If you have an even number of values, just average the two center ones to keep things fair and square. byjus.com
  3. Mode (Most Frequent Value) - The mode is all about popularity: it's the value that pops up most often in your dataset. A group can have one mode, more than one, or even no mode at all if everything appears just once. byjus.com
  4. When to Use Each Measure - Pick the mean when your data is nicely balanced without extreme outliers, go for the median if you've got wild values skewing your results, and choose the mode to find the most common category in your data. scribbr.com
  5. Effect of Outliers - Outliers are those oddballs that can pull the mean way up or down, making it tricky to see the true center. The median laughs in their face - it stays steady even when extreme values show up to the party. scribbr.com
  6. Calculating Mean for Grouped Data - For grouped data, you treat each class interval like a mini dataset: multiply each midpoint by its frequency, sum up those products, and divide by the total frequency. This method gives you a reliable mean even when you only have ranges. geeksforgeeks.org
  7. Median in Even and Odd Datasets - When there's an odd number of observations, the median is just the single middle value. If your dataset has an even count, you take the two middle numbers and average them to find a fair splitter. byjus.com
  8. Mode in Different Datasets - Datasets can be unimodal (one mode), bimodal (two), or even multimodal (many!), depending on how often values repeat. If no value ever repeats, congrats - you're in the "no mode" club. byjus.com
  9. Empirical Relationship - In moderately skewed distributions, a handy rule of thumb links mean, median, and mode: Mode ≈ 3×Median − 2×Mean. This empirical shortcut lets you estimate one measure if you know the other two. geeksforgeeks.org
  10. Understanding Skewness - Skewness tells you who's winning the tug-of-war between data extremes: in a right-skewed setup, mean > median > mode; flip it around for left-skewed where mode > median > mean. scribbr.com
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