Question 1

Q1: Find the mean deviation about the mean for the data in Exercises 1 and 2. 1. $4, 7, 8, 9, 10, 12, 13, 17$

Accepted Answer

Given: The data is $4, 7, 8, 9, 10, 12, 13, 17$. Number of observations, $n = 8$. To Find: The mean deviation about the mean. Solution: Step 1: Calculate the mean ($\bar{x}$). $$\bar{x} = \frac{4+7+8+9+10+12+13+17}{8} = \frac{80}{8} = 10$$ Step 2: Find the deviations of each observation from the mea...

Question 2

Q10: Find the mean deviation about the mean for the data in Exercises 9 and 10. 10.  | Height in cms | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145...

Accepted Answer

Given: A continuous frequency distribution. To Find: The mean deviation about the mean. Solution: We create a table to perform the calculations. We find the mid-point ($x_i$) for each class. | Height (cm) | Number of boys ($f_i$) | Mid-point ($x_i$) | $f_i x_i$ | |---|---|---|---| | 95-105 | 9 | 100...

Question 3

Q2: Find the mean deviation about the mean for the data in Exercises 1 and 2. 2. $38, 70, 48, 40, 42, 55, 63, 46, 54, 44$

Accepted Answer

Given: The data is $38, 70, 48, 40, 42, 55, 63, 46, 54, 44$. Number of observations, $n = 10$. To Find: The mean deviation about the mean. Solution: Step 1: Calculate the mean ($\bar{x}$). $$\bar{x} = \frac{38+70+48+40+42+55+63+46+54+44}{10} = \frac{500}{10} = 50$$ Step 2: Find the absolute deviatio...

Question 4

Q3: Find the mean deviation about the median for the data in Exercises 3 and 4. 3. $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$

Accepted Answer

Given: The data is $13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17$. Number of observations, $n = 12$. To Find: The mean deviation about the median. Solution: Step 1: Arrange the data in ascending order. $10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18$ Step 2: Calculate the median (M). Since $n=12$...

Question 5

Q4: Find the mean deviation about the median for the data in Exercises 3 and 4. 4. $36, 72, 46, 42, 60, 45, 53, 46, 51, 49$

Accepted Answer

Given: The data is $36, 72, 46, 42, 60, 45, 53, 46, 51, 49$. Number of observations, $n = 10$. To Find: The mean deviation about the median. Solution: Step 1: Arrange the data in ascending order. $36, 42, 45, 46, 46, 49, 51, 53, 60, 72$ Step 2: Calculate the median (M). Since $n=10$ (even), the medi...

Question 6

Q5: Find the mean deviation about the mean for the data in Exercises 5 and 6. 5.  | $x_{i}$ | 5 | 10 | 15 | 20 | 25 | |---|---|---|---|---|---| | $f_{i}$...

Accepted Answer

Given: A discrete frequency distribution. To Find: The mean deviation about the mean. Solution: We create a table to perform the calculations. | $x_i$ | $f_i$ | $f_i x_i$ | |---|---|---| | 5 | 7 | 35 | | 10 | 4 | 40 | | 15 | 6 | 90 | | 20 | 3 | 60 | | 25 | 5 | 125 | | Total | N=25 | $\sum f_i x_i =...

Question 7

Q6: Find the mean deviation about the mean for the data in Exercises 5 and 6. 6.  | $x_{i}$ | 10 | 30 | 50 | 70 | 90 | |---|---|---|---|---|---| | $f_{i}$...

Accepted Answer

Given: A discrete frequency distribution. To Find: The mean deviation about the mean. Solution: We create a table to perform the calculations. | $x_i$ | $f_i$ | $f_i x_i$ | |---|---|---| | 10 | 4 | 40 | | 30 | 24 | 720 | | 50 | 28 | 1400 | | 70 | 16 | 1120 | | 90 | 8 | 720 | | Total | N=80 | $\sum...

Question 8

Q7: Find the mean deviation about the median for the data in Exercises 7 and 8. 7.  | $x_{i}$ | 5 | 7 | 9 | 10 | 12 | 15 | |---|---|---|---|---|---|---| |...

Accepted Answer

Given: A discrete frequency distribution. The observations $x_i$ are already in ascending order. To Find: The mean deviation about the median. Solution: Step 1: Find the cumulative frequencies (c.f.) to locate the median. | $x_i$ | $f_i$ | c.f. | |---|---|---| | 5 | 8 | 8 | | 7 | 6 | 14 | | 9 | 2 |...

Question 9

Q8: Find the mean deviation about the median for the data in Exercises 7 and 8. 8.  | $x_{i}$ | 15 | 21 | 27 | 30 | 35 | |---|---|---|---|---|---| | $f_{i...

Accepted Answer

Given: A discrete frequency distribution. The observations $x_i$ are already in ascending order. To Find: The mean deviation about the median. Solution: Step 1: Find the cumulative frequencies (c.f.) to locate the median. | $x_i$ | $f_i$ | c.f. | |---|---|---| | 15 | 3 | 3 | | 21 | 5 | 8 | | 27 | 6...

Question 10

Q9: Find the mean deviation about the mean for the data in Exercises 9 and 10. 9.  | Income per day in ₹ | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 |...

Accepted Answer

Given: A continuous frequency distribution. To Find: The mean deviation about the mean. Solution: We create a table to perform the calculations. We first find the mid-point ($x_i$) for each class. | Income per day | Number of persons ($f_i$) | Mid-point ($x_i$) | $f_i x_i$ | |---|---|---|---| | 0-10...

NCERT Solutions