Tags Statistics

Statistics

Get insights from 119 questions on Statistics, answered by students, alumni, and experts. You may also ask and answer any question you like about Statistics

Follow Ask Question

119

Questions

Discussions

Active Users

Followers

New answer posted

4 months ago

Statistics Class 11th

31. Given that $\bar{x}$ is the mean and σ2 is the variance of n observations x₁, x₂, .,xn. Prove that the mean and variance of the observations ax₁, ax₂, ax₃, ., ax_n are a $\bar{x}$ and a₂ σ₂, respectively, (a ≠ 0).

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

31. For n observations x₁, x₂,……., x_n .

We have mean = $\bar{x} = \frac{\sum_{i = 1}^{n} x_{i}}{n} (1)$

and variance = $σ^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2} (2)$

Let y_i be the new observations with same n.

So, y_i = ax_i (3)

Now mean, $\bar{y} = \frac{\sum_{i = 1}^{n} y_{i}}{n} = \frac{\sum_{i = 1}^{n} a x_{i}}{n} = \frac{a \sum_{i = 1}^{n} y_{i}}{n} = a \bar{x} [(1)]$

So $\bar{y} = a \bar{x} (4)$

And, putting (3) and (4) in (2) we get,

$σ^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(\frac{y_{i}}{a} - \frac{\bar{y}}{a})}^{2}$

$\Rightarrow σ^{2} = \frac{1}{a^{2}} [\frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2}]$

$\Rightarrow {(σ^{'})}^{2} = σ^{2} α^{2} .$

Hence, the mean and variance of ax₁, ax₂, ……, ax_n are $a \bar{x}$ and a² σ² .

0 0

New answer posted

4 months ago

Statistics Class 11th

30. 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.

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

30. Let 'x' be the given observations with n = 6.

0 0

New question posted

4 months ago

Statistics Class 11th

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

0 Follower 3 Views

New question posted

4 months ago

Statistics Class 11th

Class 11 Maths Statistics Miscellaneous exercise Solution

28. 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.

0 Follower 4 Views

New answer posted

4 months ago

Statistics Class 11th

27. The sum and sum of squares corresponding to length x (in cm) and weight y (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?

0 Follower 2 Views

Payal Gupta

Contributor-Level 10

27. Given, n=50.

$\begin{array}{l} \sum_{i = 1}^{n} x i = 212 \sum_{i = 1}^{50} x i^{2} = 902.8 \end{array}$

$\sum_{i = 1}^{50} y i = 261 \sum_{i = 1}^{50} y i^{2} = 1457.6$

So, $\bar{x} = \frac{\sum_{i = 1}^{50} x_{i}}{n} = \frac{212}{50} = 4.24$

0 0

New answer posted

4 months ago

Statistics Class 11th

26. The following is the record of goals scored by team A in a football session:

No. of goals scored	0	1	2	3	4
No. of matches	1	9	7	5	3

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

0 Follower 1 View

Payal Gupta

Contributor-Level 10

26. For team A.

Hence, we conclude that team A is more consistent.

0 0

New answer posted

4 months ago

Statistics Class 11th

25. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

Firm A Firm B

No. of wage earners 586 &

...more

0 Follower 6 Views

Payal Gupta

Contributor-Level 10

(i) The number of wage earner in firm A, n_A=586. Mean monthly wages of firm

Total no of were canner in firm B.

Total monthly mages in firm. B = ?5253 * n_B

=? 5253 * 586

=? 34, 03, 944

Firm B pays larger amount of monthly wages.

(ii) Since both the firm A and B has same mean monthly wages the firm with greater standard duration i.e, greater variance will have more variability in individual ways. Therefore, firm B will have more variability in individual wages.

0 0

New answer posted

4 months ago

Statistics Class 11th

24. From the prices of shares X and Y below, find out which is more stable in value: