Answers:
Q.1 B. 6.88.
Q2. Sorry Not clearly visible its blurred
Q3. The closest answer choice is C. 4.9
Q4. 2.94
Q5. Set B
Q6. C
Explanation:
Q1.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 32, 43, 38, 28, 51
Mean = (32 + 43 + 38 + 28 + 51) / 5 = 38.4
Next, we need to find the absolute deviations of each number from the mean
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 6.88
Therefore, the answer is B. 6.88.
Q3.
To find the mean absolute deviation, we first need to find the mean of the data set
Data: 12.7, 22, 23.5, 24, 11, 22
Mean = (12.7 + 22 + 23.5 + 24 + 11 + 22) / 6= 18.2
Next, we need to find the absolute deviations of each number from the mean
|12.7 - 18.2| = 5.5
|22 - 18.2| = 3.8
|23.5 - 18.2| = 5.3
|24 - 18.2| = 5.8
|11 - 18.2| = 7.2
|22 - 18.2| = 3.8
To find the mean absolute deviation, we need to take the average of these absolute deviations
Mean Absolute Deviation = (5.5 + 3.8 + 5.3 + 5.8 + 7.2 + 3.8) / 6 = 5.9
Therefore, the closest answer choice is C. 4.9. However, this answer is not correct as the calculated value is 5.9.
Q4.
To find the average distance of these points from the mean of the data, we need to first find the mean of the data.
The mean of the data can be found by adding up all the values and dividing by the total number of values:
Mean = (-8 + 6.2 + 2.5 + 12 - 2 - 1.3 + 15 - 2 + 0 + 7) / 10
= 29.4 / 10
= 2.94
The average distance from the mean is found by taking the absolute value of the difference between each value and the mean, adding them up, and dividing by the total number of values:
Average Distance from Mean = (|(-8) - 2.94| + |6.2 - 2.94| + |2.5 - 2.94| + |12 - 2.94| + |-2 - 2.94| + |-1.3 - 2.94| + |15 - 2.94| + |-2 - 2.94| + |0 - 2.94| + |7 - 2.94|) / 10
= (10.94 + 3.26 + 0.44 + 9.06 + 4.94 + 4.24 + 12.06 + 4.94 + 2.94 + 4.06) / 10
= 5.688
Therefore, the average distance of these points from the mean of the data is 5.688, which is option D.
Q5.
o find out if the mean and median are equal in a set of data, we need to calculate both the mean and median and compare them.
Mean is calculated by adding up all the values and dividing by the total number of values.
Median is the middle value of the data when it is arranged in order.
Let's calculate the mean and median of both data sets:
A. (5, 3, 5, 8, 2, 5)
Mean = (5 + 3 + 5 + 8 + 2 + 5) / 6
= 4.6667
To calculate the median, we first need to arrange the data in order:
2, 3, 5, 5, 5, 8
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set A are not equal (4.6667 ≠ 5), set A is not the correct answer.
B. (7, 3, 5, 11, 5, 3)
Mean = (7 + 3 + 5 + 11 + 5 + 3) / 6
= 5.8333
To calculate the median, we first need to arrange the data in order:
3, 3, 5, 5, 7, 11
Since the data set has an even number of values, the median is the average of the middle two values:
Median = (5 + 5) / 2
= 5
Since the mean and median of set B are equal (5.8333 ≈ 5), set B is the correct answer.
Therefore, the set of data in which the mean and median are equal is set B: (7, 3, 5, 11, 5, 3). Answer: B.
Q6.
To answer this question, we need to first find the mean, median, and range of the data:
Data: 10, 23, 52, 18, 5, 60, 35
Mean = (10 + 23 + 52 + 18 + 5 + 60 + 35) / 7
= 28.57
Median = 23
To find the range, we need to subtract the smallest value from the largest value:
Range = 60 - 5
= 55
Now, let's evaluate each statement:
A. The mean is greater than the range.
- 28.57 > 55
- This statement is false.
B. The range is 50.
- The range is 55, not 50.
- This statement is false.
C. The median is less than the mean.
- The median is 23 and the mean is 28.57
- This statement is true.
D. The median is greater than the range.
- 23 > 55
- This statement is false.
Therefore, the statement that is true is C. The median is less than the mean.