Section A (1 Mark each)

Q1. The abscissa of the point of intersection of the less than type and of the more than type cumulative frequency curves of a grouped data gives its:

Q2. For the following distribution:
Class: 0-5, 5-10, 10-15, 15-20, 20-25
Frequency: 10, 15, 12, 20, 9
The sum of the lower limits of the median class and modal class is:

Q3. If the mode of a distribution is 8 and its mean is 8, then its median is:

Q4. Assertion (A): If the number of observations $n$ is even, then the median is the mean of $(\frac{n}{2})^{th}$ and $(\frac{n}{2}+1)^{th}$ observations.
Reason (R): The median divides the data into two equal parts.

Section B (2 Marks each)

Q5. The mean of 20 numbers is 18. If 2 is added to each number, what will be the new mean?

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Q6. Find the class mark of the class 10-25 and 35-55.

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Q7. In a frequency distribution, if $a = \text{assumed mean} = 55$, $\sum f_i = 100$, $h = 10$ and $\sum f_i u_i = -30$, then find the mean of the distribution.

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Section C (3 Marks each)

Q8. The mean of the following data is 53. Find the value of $f_1$ and $f_2$.
Class: 0-20, 20-40, 40-60, 60-80, 80-100
Frequency: 15, $f_1$, 21, $f_2$, 17
Total frequency is 100.

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Q9. Find the mode of the following distribution:
Marks: 0-10, 10-20, 20-30, 30-40, 40-50
No. of Students: 4, 8, 10, 20, 8

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Section D (5 Marks)

Q10. If the median of the distribution given below is 28.5, find the values of $x$ and $y$.
Class Interval: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequency: 5, $x$, 20, 15, $y$, 5
Total frequency is 60.

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Section E (4 Marks)

Q11. Case Study: Electricity Consumption

A survey on the daily electricity consumption (in units) of 50 households in a locality was conducted and the data is recorded as follows:

Consumption (Units) 0-2 2-4 4-6 6-8 8-10
No. of Households 4 12 14 12 8

(i) Find the modal class of the data.

(ii) Calculate the mean daily electricity consumption.

(iii) Calculate the median daily electricity consumption.

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