30 Questions
What is the formula for calculating the arithmetic mean of discrete data?
Sum of all products of values and frequencies divided by the total frequency
In grouped data, the arithmetic mean is calculated by taking the sum of:
All products of midpoints and frequencies
What is the arithmetic mean of the given discrete data with respective frequencies: 10, 20, 30, 40, 50, 60, 70?
42.35
If a new firm with monthly sales of 45 falls within the class interval, what would be considered as its representative average value?
47.5
What will happen to the arithmetic mean if an extra firm with lower sales value is added in continuous data?
It will decrease
What is the demerit of calculating the mean for a dataset?
It is not calculated in case of open end interval
In an odd number of observations, how is the median calculated for ungrouped data?
Middle observation
What is a common misconception about the mode in a set of data?
Mode is easy to calculate for continuous data
How is the median calculated for continuous data?
$l_1 + \frac{(N/2 - cf) \times h}{f}$
What does the median represent in a dataset?
The value that divides the distribution into two equal parts
What is the mode of the given data set?
33.67
What is a key demerit of the mode as explained in the text?
It is not based on all observations
What is the formula to calculate variance for ungrouped data?
$rac{1}{n} imes ext{sum}(x_i - ar{x})^2$
How is the standard deviation related to the variance?
Standard deviation is the square root of the variance
What does the range measure in a dataset?
Spread between the lowest and highest values
What does a larger standard deviation indicate?
Data points are spread out over a wider range
How is the median calculated for grouped data?
Formula involving cumulative frequencies and class intervals
What does positive kurtosis indicate about a distribution?
The distribution is more peaked than normal
How is skewness measured for ungrouped data?
Formula involving sample standard deviation and data points
In statistics, what does skewness measure?
Symmetry of the distribution
What is the interquartile range (IQR) of the dataset {65, 70, 75, 80, 85, 90, 95, 100}?
15
What is the mean absolute deviation (MAD) of the dataset {65, 70, 75, 80, 85, 90, 95, 100}?
10
In the context of variance and standard deviation, what does variance measure?
The average of squared differences from the mean
How do you calculate the First Quartile (Q1) of a dataset?
Average of the lower half of observations
What is the purpose of calculating the Interquartile Range (IQR) instead of using the Range?
IQR accounts for outliers better than Range
In a negatively skewed distribution, how does the median compare to the mean?
Median is greater than the mean
What does a positive coefficient of skewness indicate about a probability distribution?
The distribution is positively skewed
How does kurtosis differ in meaning between a positive and a negative value?
Positive kurtosis indicates peakedness, negative kurtosis indicates flatter distribution
What is the main reason that the median is considered a robust measure of central tendency?
It is not affected by extreme values or outliers
For a positively skewed distribution, how does the mode typically relate to the mean and median?
Mode is less than both mean and median
Explore the concept of arithmetic mean for ungrouped data, where the mean is calculated by summing all the values and dividing by the total number of observations. Discover how to calculate the mean using a practical example of monthly salaries of employees.
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