हिंदी

If x¯ is the mean of n values of x, then ∑i=1n(xi-x¯) is always equal to ______. If a has any value other than x¯, then ∑i=1n(xi-x¯)2 is ______ than ∑(xi-a)2

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प्रश्न

If `barx` is the mean of n values of x, then `sum_(i = 1)^n (x_i - barx)` is always equal to ______. If a has any value other than `barx`, then `sum_(i = 1)^n (x_i - barx)^2` is ______ than `sum(x_i - a)^2`

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उत्तर

If `barx` is the mean of n values of x, then `sum_(i = 1)^n (x_i - barx)` is always equal to 0. If a has any value other than `barx`, then `sum_(i = 1)^n (x_i - barx)^2` is less than `sum(x_i - a)^2`

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अध्याय 15: Statistics - Exercise [पृष्ठ २८३]

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एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 11
अध्याय 15 Statistics
Exercise | Q 41 | पृष्ठ २८३

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Find the mean deviation about the mean for the data.

4, 7, 8, 9, 10, 12, 13, 17


Find the mean deviation about the median for the data.

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17


Find the mean deviation about the median for the data.

36, 72, 46, 42, 60, 45, 53, 46, 51, 49


Find the mean deviation about the mean for the data.

xi 5 10 15 20 25
fi 7 4 6 3 5

Find the mean deviation about the mean for the data.

xi 10 30 50 70 90
fi 4 24 28 16 8

Find the mean deviation about the median for the data.

xi 5 7 9 10 12 15
fi 8 6 2 2 2 6

Find the mean deviation about the mean for the data.

Income per day in ₹ Number of persons
0-100 4
100-200 8
200-300 9
300-400 10
400-500 7
500-600 5
600-700 4
700-800 3

Calculate the mean deviation about the median of the observation:

3011, 2780, 3020, 2354, 3541, 4150, 5000


Calculate the mean deviation about the median of the observation:

 34, 66, 30, 38, 44, 50, 40, 60, 42, 51


Calculate the mean deviation about the median of the observation:

 22, 24, 30, 27, 29, 31, 25, 28, 41, 42


Calculate the mean deviation from the mean for the data: 

 4, 7, 8, 9, 10, 12, 13, 17


Calculate the mean deviation from the mean for the  data:

 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17


Calculate the mean deviation from the mean for the  data:

(iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

 

The lengths (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2
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In 38, 70, 48, 34, 63, 42, 55, 44, 53, 47 find the number of observations lying between

\[\bar { X } \]  − M.D. and

\[\bar { X } \]   + M.D, where M.D. is the mean deviation from the mean.


Find the mean deviation from the mean for the data:

xi 5 7 9 10 12 15
fi 8 6 2 2 2 6

Find the mean deviation from the mean for the data:

xi 5 10 15 20 25
fi 7 4 6 3 5

Find the mean deviation from the mean for the data:

Size 1 3 5 7 9 11 13 15
Frequency 3 3 4 14 7 4 3 4

Find the mean deviation from the median for the data: 

xi 74 89 42 54 91 94 35
fi 20 12 2 4 5 3 4

Compute the mean deviation from the median of the following distribution:

Class 0-10 10-20 20-30 30-40 40-50
Frequency 5 10 20 5 10

Find the mean deviation from the mean for the data:

Classes 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800
Frequencies 4 8 9 10 7 5 4 3

 


Find the mean deviation from the mean for the data:

Classes 0-10 10-20 20-30 30-40 40-50 50-60
Frequencies 6 8 14 16 4 2

Calculate mean deviation about median age for the age distribution of 100 persons given below:

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For a frequency distribution mean deviation from mean is computed by


The mean deviation of the numbers 3, 4, 5, 6, 7 from the mean is


Let \[x_1 , x_2 , . . . , x_n\]  be n observations and  \[X\]  be their arithmetic mean. The standard deviation is given by

 

The mean deviation of the data 2, 9, 9, 3, 6, 9, 4 from the mean is ______.


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Calculate the mean deviation about the mean for the following frequency distribution:

Class interval 0 – 4 4 – 8 8 – 12 12 – 16 16 – 20
Frequency 4 6 8 5 2

Calculate the mean deviation from the median of the following data:

Class interval 0 – 6 6 – 12 12 – 18 18 – 24 24 – 30
Frequency 4 5 3 6 2

Determine mean and standard deviation of first n terms of an A.P. whose first term is a and common difference is d.


Mean deviation for n observations x1, x2, ..., xn from their mean `barx` is given by ______.


The sum of squares of the deviations of the values of the variable is ______ when taken about their arithmetic mean.


Let X = {x ∈ N: 1 ≤ x ≤ 17} and Y = {ax + b: x ∈ X and a, b ∈ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to ______.


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