NCERT Class 11-Math's: Exemplar Chapter –15 Statistics Part 5
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Question 13:
Mean and standard deviation of items are and , respectively. Find the sum of all the item and the sum of the squares of the items.
Answer:
Question 14:
If for a distribution and the total number of item is , find the mean and standard deviation.
Answer:
Question 15:
Find the mean and variance of the frequency distribution given below:
Answer:
Long Answer Type
Question 16:
Calculate the mean deviation about the mean for the following frequency distribution:
Class Interval | |||||
Frequency |
Answer:
Given: the frequency distribution
To find: the mean deviation about the mean
Let us make a table of the given data and append other columns after calculations
Class Interval | Mid Value | Frequency | |
Total |
Here mean,
So the above table with more columns is as shown below,
Class Interval | Mid Value | Frequency | |||
Total |
Hence Mean Deviation becomes,
Therefore, the mean deviation about the mean of the distribution is
Question 17:
Calculate the mean deviation from the median of the following data:
Class Interval | |||||
Frequency |
Answer:
Given: the frequency distribution
To find: the mean deviation from the median
Let us make a table of the given data and append other columns after calculations
Class Interval | Mid Value | Frequency | Cumulative Frequency (c.f) |
Total |
Now, here , which is even.
Here median class term,
This observation lie in the class interval , so median can be written as,
Here , , and , substituting these values, the above equation becomes,
So the above table with more columns is as shown below,
Class Interval | Mid Value | Frequency | ||
Total |
Hence Mean Deviation becomes,
Therefore, the mean deviation about the median of the distribution is 7