28 Questions
What is the total number of observations in the given data?
51
What is the value of 'l' in the formula for calculating the median?
145
What is the percentage of girls who are taller than the median height?
50%
What is the formula for calculating the median from a frequency distribution table?
Median = l + (n / 2 - cf) / f
What is the median height of the girls in the given data?
149.03 cm
What is the characteristic of a data set with more than one value having the same maximum frequency?
Multimodal
What is the purpose of the frequency distribution table in finding the mode of ungrouped data?
To visualize the frequency of each data value
In a grouped frequency distribution, what is the term for the class with the maximum frequency?
Modal class
What is the formula to calculate the mode in a grouped frequency distribution?
Mode = l + ((f1 - f0) / (2f1 - f0 - f2)) × h
What is the assumption made while using the formula to calculate the mode in a grouped frequency distribution?
All class sizes are equal
What is the significance of the lower limit of the modal class (l) in the formula for calculating the mode?
It represents the starting point of the modal class
What is the value of the median marks when n = 26.5, l = 60, cf = 22, f = 7, and h = 10?
66.4
In the survey of the heights of 51 girls, what is the number of girls with height in the interval 140 - 145?
7
What is the type of distribution given in the survey of the heights of 51 girls?
Less than type
What is the frequency of the class interval below 140?
4
What is the total number of girls in the survey?
51
What is the formula used to calculate the median in the given problems?
Median = l + (h / f) * (n - cf)
What is the purpose of converting the data into continuous classes in question 4?
To find the median of the data
What is the total number of policy holders in the data given in question 3?
100
What is the range of the class interval in which the median of the distribution in question 2 lies?
20 - 30
What is the number of consumers in the class interval 125 - 145 in the frequency distribution in question 1?
20
What is the condition for a person to be eligible for a policy in the data given in question 3?
Age should be between 18 years and 60 years
What is the number of leaves in the class interval 145 - 153 in the data given in question 4?
12
What is the formula to find the mode for grouped data?
Mode = l + ((f1 - f0) / (2 * f1 - f0 - f2)) * h
What is the purpose of ensuring that the class intervals are continuous when calculating mode and median for grouped data?
To ensure the formulae can be applied correctly
What is the cumulative frequency of a class?
The frequency obtained by adding the frequencies of all the classes preceding the given class
What is the purpose of the NOTE TO THE READER in the passage?
To emphasize the importance of continuous class intervals
What is the formula for the median of grouped data?
Median = l + ((n / 2) - cf) / f * h
Study Notes
Median for Grouped Data
- The median for grouped data is calculated using the formula:
Median = l + (n/2 - cf) × h / f -
nis the total frequency,lis the lower limit of the median class,cfis the cumulative frequency of the class preceding the median class,his the class size, andfis the frequency of the median class
Example 1: Calculating Median
- Given the values:
n = 26.5,l = 60,cf = 22,f = 7, andh = 10 - The median is calculated as:
Median = 60 + (26.5 - 22) × 10 / 7 = 66.4
Example 2: Finding Median Height
- A survey of 51 girls' heights (in cm) is conducted, and the data is obtained:
Less than 140: 4,Less than 145: 11,Less than 150: 29,Less than 155: 40,Less than 160: 46, andLess than 165: 51 - The class intervals are:
Below 140,140-145,145-150,150-155,155-160, and160-165 - The frequency distribution table is constructed, and the median height is calculated using the formula:
Median = 145 + (25.5 - 11) × 5 / 18 = 149.03
Mode for Grouped Data
- The mode for grouped data is calculated using the formula:
Mode = l + (f1 - f0) × h / (2f1 - f0 - f2) -
lis the lower limit of the modal class,his the size of the class interval,f1is the frequency of the modal class,f0is the frequency of the class preceding the modal class, andf2is the frequency of the class succeeding the modal class
Example 3: Finding Mode
- The wickets taken by a bowler in 10 cricket matches are:
2, 6, 4, 5, 0, 2, 1, 3, 2, 3 - The frequency distribution table is constructed, and the mode is found to be
2
Learn how to calculate the mode of grouped data, including identifying multimodal data and understanding the concept of a single mode. This quiz covers the basics of mode calculation and its applications.
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