Measures of Central Tendency: Ungrouped Data
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Questions and Answers

What is the formula for calculating the arithmetic mean of discrete data?

  • Sum of all midpoint values divided by total number of classes
  • Sum of all frequencies divided by total frequency
  • Sum of all values divided by total number of values
  • Sum of all products of values and frequencies divided by the total frequency (correct)

In grouped data, the arithmetic mean is calculated by taking the sum of:

  • All frequencies
  • All class intervals
  • All products of midpoints and frequencies (correct)
  • All midpoint values

What is the arithmetic mean of the given discrete data with respective frequencies: 10, 20, 30, 40, 50, 60, 70?

  • 42.35 (correct)
  • 40.40
  • 39.30
  • 41.50

If a new firm with monthly sales of 45 falls within the class interval, what would be considered as its representative average value?

<p>47.5 (C)</p> Signup and view all the answers

What will happen to the arithmetic mean if an extra firm with lower sales value is added in continuous data?

<p>It will decrease (A)</p> Signup and view all the answers

What is the demerit of calculating the mean for a dataset?

<p>It is not calculated in case of open end interval (B)</p> Signup and view all the answers

In an odd number of observations, how is the median calculated for ungrouped data?

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

What is a common misconception about the mode in a set of data?

<p>Mode is easy to calculate for continuous data (D)</p> Signup and view all the answers

How is the median calculated for continuous data?

<p>$l_1 + \frac{(N/2 - cf) \times h}{f}$ (B)</p> Signup and view all the answers

What does the median represent in a dataset?

<p>The value that divides the distribution into two equal parts (B)</p> Signup and view all the answers

What is the mode of the given data set?

<p>33.67 (D)</p> Signup and view all the answers

What is a key demerit of the mode as explained in the text?

<p>It is not based on all observations (D)</p> Signup and view all the answers

What is the formula to calculate variance for ungrouped data?

<p>$rac{1}{n} imes ext{sum}(x_i - ar{x})^2$ (D)</p> Signup and view all the answers

How is the standard deviation related to the variance?

<p>Standard deviation is the square root of the variance (B)</p> Signup and view all the answers

What does the range measure in a dataset?

<p>Spread between the lowest and highest values (B)</p> Signup and view all the answers

What does a larger standard deviation indicate?

<p>Data points are spread out over a wider range (C)</p> Signup and view all the answers

How is the median calculated for grouped data?

<p>Formula involving cumulative frequencies and class intervals (A)</p> Signup and view all the answers

What does positive kurtosis indicate about a distribution?

<p>The distribution is more peaked than normal (A)</p> Signup and view all the answers

How is skewness measured for ungrouped data?

<p>Formula involving sample standard deviation and data points (B)</p> Signup and view all the answers

In statistics, what does skewness measure?

<p>Symmetry of the distribution (B)</p> Signup and view all the answers

What is the interquartile range (IQR) of the dataset {65, 70, 75, 80, 85, 90, 95, 100}?

<p>15 (C)</p> Signup and view all the answers

What is the mean absolute deviation (MAD) of the dataset {65, 70, 75, 80, 85, 90, 95, 100}?

<p>10 (A)</p> Signup and view all the answers

In the context of variance and standard deviation, what does variance measure?

<p>The average of squared differences from the mean (A)</p> Signup and view all the answers

How do you calculate the First Quartile (Q1) of a dataset?

<p>Average of the lower half of observations (B)</p> Signup and view all the answers

What is the purpose of calculating the Interquartile Range (IQR) instead of using the Range?

<p>IQR accounts for outliers better than Range (B)</p> Signup and view all the answers

In a negatively skewed distribution, how does the median compare to the mean?

<p>Median is greater than the mean (A)</p> Signup and view all the answers

What does a positive coefficient of skewness indicate about a probability distribution?

<p>The distribution is positively skewed (D)</p> Signup and view all the answers

How does kurtosis differ in meaning between a positive and a negative value?

<p>Positive kurtosis indicates peakedness, negative kurtosis indicates flatter distribution (D)</p> Signup and view all the answers

What is the main reason that the median is considered a robust measure of central tendency?

<p>It is not affected by extreme values or outliers (C)</p> Signup and view all the answers

For a positively skewed distribution, how does the mode typically relate to the mean and median?

<p>Mode is less than both mean and median (B)</p> Signup and view all the answers

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