1. The marks obtained by 10 students in a mathematics test are 75, 90, 70, 50, 70, 50, 75, 90, 70 and 75. Find their median mark?
a. 70
b. 72.5
c. 75
d. 71.5
2. The numbers 2, 3, 4, 4, 2x + 1, 7, 7, 8 and 9 are written in an ascending order. If the median is 7, then find mode of this data?
a. 8
b. 7
c. 4
d. 9
3. The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers becomes 20. The excluded number is
a. 36
b. 38
c. 37
d. 39
4. The mean of five observations is 15. If the mean of first three observations is 14 and that of last three is 17, then find the third observation?
a. 29
b. 31
c. 18
d. 32
5. The mean of 50 observations is 39. If one of the observations which was 23 was replaced by 43, what will be the resulting mean?
a. 38.4
b. 39.4
c. 39
d. 40.3
6. The traffic police recorded the speed (in km/h) of 10 motorists as 48, 52, 57, 55, 42, 39, 60, 49, 53 and 47. Later an error in recording instrument was found. If the instrument has recorded the speed 5 km/h less in each case, then find the correct average speed of the motorists?
a. 54.5 km/h
b. 52.5 km/h
c. 55.2 km/h
d. 50.2 km/h
7. When the data consists of 3, 4, 5, 4, 3, 4, 5, which statement is true?
a. Mean > mode
b. Mean = mode
c. Mean > median
d. Median < mode
8. The difference between the mean and median of first five prime numbers is
a. 0.8
b. 0.6
c. 0.4
d. 1
9. Vihaan has marks of 92, 85, and 78 in three mathematics tests. In order to have an average of exactly 87 for the four math tests, what marks he should obtain?
a. 92 marks
b. 93 marks
c. 91 marks
d. 90 marks
10. If the mean of the observations: x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of last three observations is
a. 7
b. 9
c.
d.
Chapter  14 Statistics Quiz3  Math Class 9th
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Question 1 of 10
1. Question
The marks obtained by 10 students in a mathematics test are 75, 90, 70, 50, 70, 50, 75, 90, 70 and 75. Find their median mark?
Correct
The median is the middle value for a set of data that has been arranged in ascending or descending order of magnitude.
Arrange the given observations in ascending order
50, 50, 70, 70, 70, 75, 75, 75, 90, 90
Here two numbers 70 and 75 are in the middle
So, median is average of 70 and 75 i.e. 72.5.
Incorrect
The median is the middle value for a set of data that has been arranged in ascending or descending order of magnitude.
Arrange the given observations in ascending order
50, 50, 70, 70, 70, 75, 75, 75, 90, 90
Here two numbers 70 and 75 are in the middle
So, median is average of 70 and 75 i.e. 72.5.

Question 2 of 10
2. Question
The numbers 2, 3, 4, 4, 2x + 1, 7, 7, 8 and 9 are written in an ascending order. If the median is 7, then find mode of this data?
Correct
The median is the middle score for a set of data that has been arranged in ascending or descending order of magnitude.
Since 2x+1 is in the middle of the arranged numbers, so it is median
Hence, 2x+1= 7
Now since 7 occurs more number of times then other numbers so mode of the list is 7
Incorrect
The median is the middle score for a set of data that has been arranged in ascending or descending order of magnitude.
Since 2x+1 is in the middle of the arranged numbers, so it is median
Hence, 2x+1= 7
Now since 7 occurs more number of times then other numbers so mode of the list is 7

Question 3 of 10
3. Question
The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers becomes 20. The excluded number is
Correct
The mean of six numbers is 23
So sum of six numbers is 23×6 = 138
After excluding one number, the mean of the remaining numbers is 20
So sum of five numbers is 20 × 5 =100
The difference between them is
138 – 100 = 38
Incorrect
The mean of six numbers is 23
So sum of six numbers is 23×6 = 138
After excluding one number, the mean of the remaining numbers is 20
So sum of five numbers is 20 × 5 =100
The difference between them is
138 – 100 = 38

Question 4 of 10
4. Question
The mean of five observations is 15. If the mean of first three observations is 14 and that of last three is 17, then find the third observation?
Correct
The mean of five observations is 15
So sum of these five observation is 15 × 5 = 75
The mean of first three observations is 14
So sum of first three observations is 14 × 3 = 42
So the sum of last two numbers is 75 – 42 = 33
The mean of last three observations is 17
So sum of last three observations is 17 × 3 = 51
So the middle number is 5133 = 18
Incorrect
The mean of five observations is 15
So sum of these five observation is 15 × 5 = 75
The mean of first three observations is 14
So sum of first three observations is 14 × 3 = 42
So the sum of last two numbers is 75 – 42 = 33
The mean of last three observations is 17
So sum of last three observations is 17 × 3 = 51
So the middle number is 5133 = 18

Question 5 of 10
5. Question
The mean of 50 observations is 39. If one of the observations which was 23 was replaced by 43, what will be the resulting mean?
Correct
The mean of 50 observations is 39.
So sum of these 50 observations is 50 × 39 = 1950
After replacing the observation value 23 by 43,
Sum becomes 1970
So the mean is 1970/50 = 39.4
Incorrect
The mean of 50 observations is 39.
So sum of these 50 observations is 50 × 39 = 1950
After replacing the observation value 23 by 43,
Sum becomes 1970
So the mean is 1970/50 = 39.4

Question 6 of 10
6. Question
The traffic police recorded the speed (in km/h) of 10 motorists as 48, 52, 57, 55, 42, 39, 60, 49, 53 and 47. Later an error in recording instrument was found. If the instrument has recorded the speed 5 km/h less in each case, then find the correct average speed of the motorists?
Correct
Sum of all the recorded speeds is
48+52+57+55+42+39+60+49+53+47 = 502
Because of the error, 5 km/h in each case
The sum increases by 50, so the new sum is 552.
So the average speed of 10 vehicle is 55.2 km/h.
Incorrect
Sum of all the recorded speeds is
48+52+57+55+42+39+60+49+53+47 = 502
Because of the error, 5 km/h in each case
The sum increases by 50, so the new sum is 552.
So the average speed of 10 vehicle is 55.2 km/h.

Question 7 of 10
7. Question
When the data consists of 3, 4, 5, 4, 3, 4, 5, which statement is true?
Correct
The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.
Mean of the given data is 4
The mode in a list of numbers refers to the integers that occurs most number of times.
So mode is also 4
Hence mean = mode
Incorrect
The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.
Mean of the given data is 4
The mode in a list of numbers refers to the integers that occurs most number of times.
So mode is also 4
Hence mean = mode

Question 8 of 10
8. Question
The difference between the mean and median of first five prime numbers is
Correct
Incorrect

Question 9 of 10
9. Question
Vihaan has marks of 92, 85, and 78 in three mathematics tests. In order to have an average of exactly 87 for the four math tests, what marks he should obtain?
Correct
Incorrect

Question 10 of 10
10. Question
If the mean of the observations: x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of last three observations is