मराठी

The Sum and Sum of Squares Corresponding to Length X (In Cm) and Weight Y (In Gm) of 50 Plant Products Are Given Below: - Mathematics

Advertisements
Advertisements

प्रश्न

The sum and sum of squares corresponding to length (in cm) and weight (in gm) of 50 plant products are given below:

`sum_(i-1)^50 x_i = 212, sum_(i=1)^50 x_i^2 = 902.8, sum_(i=1)^50 y_i = 261, sum_(i = 1)^50 y_i^2 = 1457.6`

Which is more varying, the length or weight?

 

उत्तर

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 15: Statistics - Exercise 15.3 [पृष्ठ ३७६]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 11
पाठ 15 Statistics
Exercise 15.3 | Q 5 | पृष्ठ ३७६

संबंधित प्रश्‍न

Find the mean and variance for the data.

6, 7, 10, 12, 13, 4, 8, 12


Find the mean and variance for the first n natural numbers.


Find the mean and variance for the data.

xi 92 93 97 98 102 104 109
fi 3 2 3 2 6 3 3

The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.


The mean and variance of 7 observations are 8 and 16, respectively. If five of the observations are 2, 4, 10, 12 and 14. Find the remaining two observations.


The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations


The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

  1. If wrong item is omitted.
  2. If it is replaced by 12.

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Subject

Mathematics

Physics

Chemistry

Mean

42

32

40.9

Standard deviation

12

15

20

Which of the three subjects shows the highest variability in marks and which shows the lowest?


The mean and standard deviation of 6 observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.


The mean and variance of 8 observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

 

For a group of 200 candidates, the mean and standard deviations of scores were found to be 40 and 15 respectively. Later on it was discovered that the scores of 43 and 35 were misread as 34 and 53 respectively. Find the correct mean and standard deviation.

 

The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:
(i) If wrong item is omitted
(ii) if it is replaced by 12.


Show that the two formulae for the standard deviation of ungrouped data 

\[\sigma = \sqrt{\frac{1}{n} \sum \left( x_i - X \right)^2_{}}\] and 

\[\sigma' = \sqrt{\frac{1}{n} \sum x_i^2 - X^2_{}}\]  are equivalent, where \[X = \frac{1}{n}\sum_{} x_i\]

 

 

Find the standard deviation for the following data:

x : 3 8 13 18 23
f : 7 10 15 10 6

A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and S.D.


Calculate the mean, median and standard deviation of the following distribution:

Class-interval: 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70
Frequency: 2 3 8 12 16 5 2 3

Find the mean and variance of frequency distribution given below:

xi: 1 ≤ < 3 3 ≤ < 5 5 ≤ < 7 7 ≤ < 10
fi: 6 4 5 1

Mean and standard deviation of 100 observations were found to be 40 and 10 respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.      


Two plants A and B of a factory show following results about the number of workers and the wages paid to them 

  Plant A Plant B
No. of workers 5000 6000
Average monthly wages Rs 2500 Rs 2500
Variance of distribution of wages 81 100

In which plant A or B is there greater variability in individual wages?

 

 


Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?


The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, physics and chemistry are given below: 

Subject Mathematics Physics Chemistry
Mean 42 32 40.9
Standard Deviation 12 15 20

Which of the three subjects shows the highest variability in marks and which shows the lowest?

 

From the data given below state which group is more variable, G1 or G2?

Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Group G1 9 17 32 33 40 10 9
Group G2 10 20 30 25 43 15 7

If X and Y are two variates connected by the relation

\[Y = \frac{aX + b}{c}\]  and Var (X) = σ2, then write the expression for the standard deviation of Y.
 
 

In a series of 20 observations, 10 observations are each equal to k and each of the remaining half is equal to − k. If the standard deviation of the observations is 2, then write the value of k.


If each observation of a raw data whose standard deviation is σ is multiplied by a, then write the S.D. of the new set of observations.

 

If v is the variance and σ is the standard deviation, then

 


The standard deviation of first 10 natural numbers is


Show that the two formulae for the standard deviation of ungrouped data.

`sigma = sqrt((x_i - barx)^2/n)` and `sigma`' = `sqrt((x^2_i)/n - barx^2)` are equivalent.


Life of bulbs produced by two factories A and B are given below:

Length of life
(in hours)
Factory A
(Number of bulbs)
Factory B
(Number of bulbs)
550 – 650 10 8
650 – 750 22 60
750 – 850 52 24
850 – 950 20 16
950 – 1050 16 12
  120 120

The bulbs of which factory are more consistent from the point of view of length of life?


Find the standard deviation of the first n natural numbers.


The mean and standard deviation of a set of n1 observations are `barx_1` and s1, respectively while the mean and standard deviation of another set of n2 observations are `barx_2` and  s2, respectively. Show that the standard deviation of the combined set of (n1 + n2) observations is given by

S.D. = `sqrt((n_1(s_1)^2 + n_2(s_2)^2)/(n_1 + n_2) + (n_1n_2 (barx_1 - barx_2)^2)/(n_1 + n_2)^2)`


The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.


If for distribution `sum(x - 5)` = 3, `sum(x - 5)^2` = 43 and total number of items is 18. Find the mean and standard deviation.


Let x1, x2, ... xn be n observations. Let wi = lxi + k for i = 1, 2, ...n, where l and k are constants. If the mean of xi’s is 48 and their standard deviation is 12, the mean of wi’s is 55 and standard deviation of wi’s is 15, the values of l and k should be ______.


Standard deviations for first 10 natural numbers is ______.


The standard deviation of a data is ______ of any change in orgin, but is ______ on the change of scale.


The standard deviation is ______to the mean deviation taken from the arithmetic mean.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×