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</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</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</p> Signup and view all the answers

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

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

    How is the median calculated for continuous data?

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

    What is the mode of the given data set?

    <p>33.67</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</p> Signup and view all the answers

    What is the formula to calculate variance for ungrouped data?

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

    What does the range measure in a dataset?

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

    What does a larger standard deviation indicate?

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

    How is the median calculated for grouped data?

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

    What does positive kurtosis indicate about a distribution?

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

    How is skewness measured for ungrouped data?

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

    In statistics, what does skewness measure?

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

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