High School

11. The sum of deviations of a certain number of observations measured from 4 is 72, and that measured from 7 is -3. Find the number of observations and their mean.

12. The rate of GST as a percentage of sales, paid by 400 shopkeepers of a market during an assessment year, ranged from 0 to 25%. The GST paid by 18% of them was not greater than 5%. The median rate of GST was 10%, and the 75th percentile rate of GST was 15%. If only 8% of shopkeepers paid GST at a rate greater than 20% but not greater than 25%, summarize the information in the frequency distribution, taking intervals of 5%. Also, find the Mean and Mode.

13. The Geometric Mean (GM) of 8 items is 3, and that of 12 items is 11. What will be the GM of all 20 items?

14. Use an appropriate measure to evaluate the variation in the following data:
- Fire Size (in acres): Below 40, 41-80, 81-120, 121-400, 161-300, 301-340, 241
- Number of Firms: 39, 44, 61, 39, 13, 34, 169, 113, 145

15. For a group of 50 male workers, the mean and standard deviation of their monthly wages are ₹6300 and ₹900, respectively. For a group of 40 female workers, these are ₹5400 and ₹600, respectively. Find the combined standard deviation of monthly wages for all the workers.

16. From the analysis of monthly wages paid to the employees in two organizations X and Y, the following results were obtained:
- Average monthly wages (₹): X = 1600, Y = 1348.5
- Variance of distribution of wages: X = 100, Y = su1

a. Which organization pays a larger amount as monthly wages?

b. In which organization is there greater variability in the individual wages?

c. Find the combined standard deviation of both the organizations.

17. Compute the Mean and Standard Deviation from the following frequency distribution. Also, adjust the marks to obtain a Mean of 50 and a Standard Deviation of 20.
- Roll No: 1, 2, 3, 4, 5
- Frequency: 8, 12, 46, 15

18. Mean and Standard Deviation of 200 items are given as 60 and 12, respectively. Later on, it was found that 13 and 17 were incorrectly written as 3 and 67, respectively. Find the corrected Mean and Standard Deviation.

19. Mean and Standard Deviation of 100 items are given as 35 and 4, respectively. If the items 32, 34, and 39 are omitted from the series, find the corrected Mean and Standard Deviation for the remaining series.

20. From the following data relating to two series, find out the Standard Deviation in a combined manner.

Answer :

Final answer:

There is no specific number of observations that satisfies the given conditions.

Explanation:

To find the number of observations and their mean, we can use the concept of deviations and the formula for calculating the mean.

Let's denote the number of observations as 'n'.

Given that the sum of deviations from 4 is 72 and the sum of deviations from 7 is -3.

We can set up the following equations:

n * mean deviation from 4 = 72

n * mean deviation from 7 = -3

From the fact mentioned earlier, we know that the sum of deviations from a given value is equal to the product of the number of observations and the mean deviation.

So, we can rewrite the equations as:

n * mean deviation from 4 = 72

n * mean deviation from 7 = -3

Dividing both equations by 'n', we get:

mean deviation from 4 = 72 / n

mean deviation from 7 = -3 / n

Since the mean deviation is the average of the deviations from the given value, we can set up the following equation:

(mean deviation from 4 + mean deviation from 7) / 2 = mean deviation

Substituting the values, we get:

(72 / n + (-3 / n)) / 2 = mean deviation

Simplifying the equation, we get:

(69 / n) / 2 = mean deviation

69 / (2n) = mean deviation

Now, we can substitute the mean deviation back into the original equations:

n * (69 / (2n)) = 72

n * (69 / (2n)) = -3

Simplifying the equations, we get:

69 / 2 = 72

69 / 2 = -3

Since the second equation is not possible, we can ignore it.

From the first equation, we can solve for 'n':

69 / 2 = 72

69 = 2 * 72

69 = 144

Since the equation is not true, there is no solution for 'n'.

Therefore, there is no specific number of observations that satisfies the given conditions.

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