Q1.
What is the mean of the following data set: 15, 20, 25, 30, 35?
- 20
- 25
- 30
- 35
Show answer
Answer: B. 25
The mean is calculated as the sum of all observations divided by the number of observations.
Mean = (15 + 20 + 25 + 30 + 35) / 5
Mean = 125 / 5
Mean = 25
Q2.
Find the mode of the data: 7, 9, 12, 7, 15, 9, 7, 18, 20.
- 9
- 7
- 12
- 15
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Answer: B. 7
The mode is the value that appears most frequently in a data set.
In the given data: 7 appears 3 times, 9 appears 2 times, and other numbers appear once.
Therefore, the mode is 7.
Q3.
What is the median of the data: 12, 8, 15, 10, 18, 5, 20?
- 10
- 12
- 15
- 8
Show answer
Answer: B. 12
To find the median, first arrange the data in ascending order:
5, 8, 10, 12, 15, 18, 20
Number of observations (n) = 7 (which is an odd number).
The median is the ((n+1)/2)th observation.
Median = ((7+1)/2)th = 4th observation.
The 4th observation in the sorted list is 12.
Q4.
Calculate the mean of the following frequency distribution:
Value (x): 5, 10, 15, 20
Frequency (f): 3, 2, 4, 1
- 11
- 11.5
- 12
- 12.5
Show answer
Answer: B. 11.5
The mean for a frequency distribution is calculated using the formula: Mean = Sum(f*x) / Sum(f)
First, calculate f*x for each value:
(5 * 3) = 15
(10 * 2) = 20
(15 * 4) = 60
(20 * 1) = 20
Sum(f*x) = 15 + 20 + 60 + 20 = 115
Next, calculate the sum of frequencies:
Sum(f) = 3 + 2 + 4 + 1 = 10
Mean = 115 / 10 = 11.5
Q5.
Find the median of the data: 24, 28, 20, 32, 26, 30.
- 26
- 27
- 28
- 29
Show answer
Answer: B. 27
To find the median, first arrange the data in ascending order:
20, 24, 26, 28, 30, 32
Number of observations (n) = 6 (which is an even number).
For an even number of observations, the median is the average of the (n/2)th and ((n/2)+1)th observations.
Median = ( (6/2)th observation + ((6/2)+1)th observation ) / 2
Median = ( 3rd observation + 4th observation ) / 2
The 3rd observation is 26, and the 4th observation is 28.
Median = (26 + 28) / 2 = 54 / 2 = 27.
Q6.
If the mean and median of a moderately skewed distribution are 30 and 32 respectively, what is the approximate mode?
- 34
- 35
- 36
- 38
Show answer
Answer: C. 36
For a moderately skewed distribution, the empirical relationship between mean, median, and mode is given by:
Mode ≈ 3 * Median - 2 * Mean
Given Mean = 30 and Median = 32.
Mode = 3 * 32 - 2 * 30
Mode = 96 - 60
Mode = 36
Q7.
The mean of 5 numbers is 40. If four of the numbers are 30, 35, 45, 50, what is the fifth number?
- 30
- 35
- 40
- 45
Show answer
Answer: C. 40
The formula for mean is: Mean = Sum of observations / Number of observations
So, Sum of observations = Mean * Number of observations
Total sum of 5 numbers = 40 * 5 = 200.
Sum of the four given numbers = 30 + 35 + 45 + 50 = 160.
Fifth number = Total sum - Sum of four numbers
Fifth number = 200 - 160 = 40.
Q8.
The average weight of 20 students in a class is 45 kg. The average weight of another class of 30 students is 50 kg. What is the average weight of all 50 students combined?
- 47 kg
- 47.5 kg
- 48 kg
- 48.5 kg
Show answer
Answer: C. 48 kg
Total weight of the first class (20 students) = Number of students * Average weight = 20 * 45 kg = 900 kg.
Total weight of the second class (30 students) = Number of students * Average weight = 30 * 50 kg = 1500 kg.
Total number of students = 20 + 30 = 50.
Total weight of all students combined = 900 kg + 1500 kg = 2400 kg.
Combined average weight = Total weight / Total number of students = 2400 kg / 50 = 48 kg.
Q9.
The mean of 10 observations was calculated as 50. Later, it was found that one observation, 65, was wrongly copied as 55. What is the correct mean?
- 49
- 50
- 51
- 52
Show answer
Answer: C. 51
Incorrect sum of observations = Incorrect Mean * Number of observations = 50 * 10 = 500.
The incorrect observation was 55, and the correct observation should have been 65.
To find the correct sum, we subtract the wrong value and add the correct value:
Correct sum of observations = Incorrect sum - Wrong value + Correct value
Correct sum of observations = 500 - 55 + 65 = 500 + 10 = 510.
Number of observations remains 10.
Correct Mean = Correct sum / Number of observations = 510 / 10 = 51.
Q10.
A survey recorded the number of books read by 25 students in a month. The data is as follows:
Number of books (x): 0, 1, 2, 3, 4, 5
Number of students (f): 2, 5, 8, 6, 3, 1
What is the median number of books read?
- 2
- 2.5
- 3
- 3.5
Show answer
Answer: A. 2
To find the median from a frequency distribution, we first calculate the cumulative frequency (cf).
x | f | cf
--|---|---
0 | 2 | 2
1 | 5 | 7
2 | 8 | 15
3 | 6 | 21
4 | 3 | 24
5 | 1 | 25
Total number of observations (n) = Sum(f) = 25 (which is an odd number).
The median position is (n+1)/2 = (25+1)/2 = 13th observation.
Now, we look for the cumulative frequency that is just greater than or equal to the 13th observation.
From the cf column, 15 is the first cumulative frequency greater than or equal to 13. The value of x corresponding to cf = 15 is 2.
Therefore, the median number of books read is 2.
