Measures of Central Tendency Quiz
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Questions and Answers

What is the median of the following swim times: 2.6, 7.2, 3.5, 9.8, 2.5, 3.5 minutes?

  • 7.2 minutes
  • 5.85 minutes
  • 2.6 minutes
  • 3.5 minutes (correct)

What is the mode of the following data: 7, 13, 18, 24, 9, 3, 18?

  • 13
  • There is no mode
  • 18 (correct)
  • 7

What is the median age of the 10 subjects in the study with the following ages: 34, 24, 56, 52, 21, 44, 64, 34, 42, 46?

  • 43 years
  • 40 years
  • 42 years (correct)
  • 44 years

What is the mean age of the 10 subjects in the study with the following ages: 34, 24, 56, 52, 21, 44, 64, 34, 42, 46?

<p>39 years (D)</p> Signup and view all the answers

What is the mode of the ages in the following data set: 3, 7, 9, 13, 18, 18, 24?

<p>18 years (C)</p> Signup and view all the answers

What is the mean of the given data set: {1, 3, 6, 7, 2, 3, 5}?

<p>3.9 (C)</p> Signup and view all the answers

If a data set has a mean of 2.6 with the frequencies provided, what is the total sum of (f * Y)?

<p>3526 (A)</p> Signup and view all the answers

What is the definition of the median in a set of data?

<p>The middle value when data is arranged in order (C)</p> Signup and view all the answers

In a set of numbers where n is odd, how is the median calculated?

<p>It is the middle number in the data set (B)</p> Signup and view all the answers

When there are two middle numbers in a set of data, how is the median calculated?

<p>It is the average of the two middle numbers (A)</p> Signup and view all the answers

What was Nick's median quiz score during the first marking period given these scores: 90, 92, 93, 88, 95, 88, 97, and 87?

<p>91.5 (B)</p> Signup and view all the answers

What is the formula for calculating the arithmetic mean of a population?

<p>$\mu = \frac{\sum_{i=1}^{N} x_i}{N}$ (B)</p> Signup and view all the answers

Which measure of central tendency is defined as the value that divides the distribution in half when observations are ordered?

<p>Median (C)</p> Signup and view all the answers

If a data set contains the values {2, 4, 6, 8, 10}, what is the mode?

<p>All values appear with equal frequency, so there is no mode. (D)</p> Signup and view all the answers

If the arithmetic mean of a sample is denoted by $\bar{X}$, what is the correct formula for calculating it?

<p>$\bar{X} = \frac{\sum_{i=1}^{n} x_i}{n}$ (C)</p> Signup and view all the answers

If a data set contains the values {3, 3, 5, 5, 5, 7, 9}, what is the median?

<p>5 (B)</p> Signup and view all the answers

Which of the following statements is true about measures of central tendency?

<p>The mean, median, and mode can have different values for the same data set. (C)</p> Signup and view all the answers

Flashcards

Median Swim Time

Average of two middle values in sorted swim times of 2.6, 7.2, 3.5, 9.8, 2.5, 3.5 minutes is 3.5 mins.

Mode in Data Set

The mode of a data set is the value that appears most frequently; for 7, 13, 18, 24, 9, 3, 18, it's 18.

Median Age Calculation

Median age of ages 34, 24, 56, 52, 21, 44, 64, 34, 42, 46 is the average of two middle values, 42.

Mean Age Calculation

Mean age for subject ages is calculated as total sum of ages divided by the number of subjects, which is 42.5.

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Mode of Ages

In the age data set 3, 7, 9, 13, 18, 18, 24, the mode is 18, occurring twice.

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Mean Calculation

The mean for the set {1, 3, 6, 7, 2, 3, 5} is approximately 3.86, calculated by total sum divided by the count.

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Total Sum of Frequencies

Total sum from a data set's mean and frequencies is mean times total frequency, given mean is 2.6.

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Definition of Median

The median is the middle value in a data set arranged in numerical order.

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Calculating Median for Odd Set

For an odd number of observations, the median is the value at position (n + 1)/2.

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Calculating Median for Even Set

For an even set, the median is the average of the two central numbers.

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Nick's Quiz Score Median

To find median from Nick's scores (90, 92, 93, 88, 95, 88, 97, 87), sort then average the two middle scores.

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Arithmetic Mean Formula

Mean (μ) is calculated using Sum of all values divided by Number of values for a population.

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Central Tendency Definition

Central tendency measure divides distribution in half, known as median.

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Mode in Given Values

The mode for the set {2, 4, 6, 8, 10} is non-existent, as each appears once.

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Sample Mean Formula

Sample mean denoted as $ar{X}$ is calculated as $ar{X} = (ΣX) / n$ where ΣX is the total of sample values.

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Median of Data Set

The median for data set {3, 3, 5, 5, 5, 7, 9} is 5, as it's the middle value.

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True Statements About Central Tendency

Measures of central tendency summarize data sets with a single typical value, central to understanding data.

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Study Notes

Swim Times Statistics

  • Median swim times for 2.6, 7.2, 3.5, 9.8, 2.5, and 3.5 minutes is the average of the two middle values in the sorted list, which is 3.5 minutes.

Mode in Data Set

  • Mode of the data set 7, 13, 18, 24, 9, 3, 18 is 18, as it appears most frequently.

Median Age Calculation

  • Median age for ages 34, 24, 56, 52, 21, 44, 64, 34, 42, 46 is the average of the two middle values in the sorted list, yielding 42.

Mean Age Calculation

  • Mean age for the subject ages 34, 24, 56, 52, 21, 44, 64, 34, 42, 46 equals to the sum of all ages divided by the number of subjects, which is 42.5.

Mode of Ages

  • Mode in the age data set 3, 7, 9, 13, 18, 18, 24 is 18.

Mean Calculation

  • Mean for the set {1, 3, 6, 7, 2, 3, 5} is calculated by dividing the sum of all numbers (27) by the count of numbers (7), resulting in approximately 3.86.

Total Sum of Frequencies

  • If a data set has a mean of 2.6 and frequencies are given, the total sum of (f * Y) equals the mean multiplied by the total frequency.

Definition of Median

  • The median is defined as the middle value in a data set when arranged in numerical order.

Calculating Median for Odd Set

  • For a data set with an odd number of observations (n), the median is the value at the position (n + 1)/2.

Calculating Median for Even Set

  • When there are two middle numbers in a data set, the median is the average of these two central values.

Nick's Quiz Score Median

  • To find Nick's median quiz score from the scores 90, 92, 93, 88, 95, 88, 97, and 87, sort the scores and find the average of the two middle scores.

Arithmetic Mean Formula

  • The formula for calculating the arithmetic mean of a population is: Mean (μ) = Sum of all values / Number of values.

Central Tendency Definition

  • The measure of central tendency that divides the distribution in half is known as the median.

Mode in Given Values

  • The mode for the set {2, 4, 6, 8, 10} is non-existent, as all values occur only once.

Sample Mean Formula

  • The arithmetic mean of a sample, denoted as $\bar{X}$, is calculated using the formula: $\bar{X} = (ΣX) / n$, where ΣX is the sum of all sample values and n is the number of samples.

Median of Data Set

  • The median for the data set {3, 3, 5, 5, 5, 7, 9} is 5, as it is the middle value in the ordered set.

True Statements About Central Tendency

  • Understanding measures of central tendency is crucial as they summarize data sets with single values that represent a typical case.

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Test your knowledge on central tendency measures such as mean, median, and mode. Learn how these values describe the average or typical of a distribution and where the middle of a dataset lies.

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