Statistics MATHS - Statistics

The wickets taken by a bowler in a one day cricket match are 4, 5, 6, 3, 4, 0, 3, 2, 3, 5. The mode of the data is ________ .

The average of 2, 4, 6, 8, 10 is .................

Find the mean of the first five multiples of 7.

If the mode of five observations, in order, 0, 2, 3, m, 5 is 3 then m = _______.

Two high school classes took the same test. One class of 20 students made an average grade of 80%; the other class of 30 students made an average grade of 70%. The average grade for all students in both classes is:

Fill in the blanks.
If the variance of a data is 121, then the standard deviation of the data is _______.

Fill in the blanks.
The sum of the squares of the deviations of the values of the variable is _______ when taken about their arithmetic mean.

Fill in the blanks.
The mean deviation of the data is _______ when measured from the median.

Fill in the blanks.
The standard deviation of a data is _________ of any change in orgin, but is _________ on the change of scale.

The mean and standard deviation of 20 observation are found to be 10 and 2 respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in cases of it is replaced by 12 .

The mean and standard deviation of 20 observation is found to be 10 and 2 respectively. On rechecking, it was found that observation 8 was incorrect. Calculate the correct mean and standard deviation in cases of the wrong items is omitted.

Find the mean and variance of the following data.

xi	92	93	97	98	102	104	109
fi	3	2	3	2	6	3	3

Find the mean and variance for each of the data

xi	6	10	14	18	24	28	30
fi	2	4	7	12	8	4	3

Find the mean and variance for: First 10 multiples of 3

Find the mean and variance for each of the data First n natural numbers.

Find the mean and variance for each of the data
6, 7, 10, 12, 13, 4, 8, 12

The mean and standard deviation of a group of 100 observation were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Subject	Mathematics	Physics	Chemistry
Mean	42	32	40.9
Standard deviation	12	15	20

Which of these three subjects shows the highest variability in marks and which shows the lowest?

The mean and standard deviation of six observation are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

The mean and variance of 7 observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12, 14 find the remaining two observations.

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) Consider the following data

xi	5	10	15	20	25
fi	7	4	6	3	5

Then, the mean deviation about the mean is 6.32.
Reason (R) Consider the following data.

xi	10	30	50	70	90
fi	4	24	28	16	8

Then, the mean deviation about the mean is 15.

1. A is true, R is true; R is acorrect explanation of A.
2. A is true, R is true; R is not a correct explanation of A.
3. A is true; R is false
4. A is false; R is true.

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is 80%.
Reason (R) Mean marks scored by the students of a class is 53. The mean marks of the girls is 55 and the mean marks of the boys is 50. The percentage of girls in the class is 64%.

1. A is true, R is true; R is acorrect explanation of A.
2. A is true, R is true; R is not a correct explanation of A.
3. A is true; R is false
4. A is false; R is true.

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A) If each of the observations x₁, x₂, ..., X_n is increased by a, where ais a negative or positive number, then the variance remains unchanged
Reason (R) Adding or subtracting a positive or negative number to (or from) each observation of a group does not affect the variance.

1. A is true, R is true; R is acorrect explanation of A.
2. A is true, R is true; R is not a correct explanation of A.
3. A is true; R is false
4. A is false; R is true.

Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Consider the following data

xi	6	10	14	18	24	28	30
fi	2	4	7	12	8	4	3

Assertion (A) The mean of the data is 19.
Reason (R) The variance of the data is 43.4.

1. A is true, R is true; R is acorrect explanation of A.
2. A is true, R is true; R is not a correct explanation of A.
3. A is true; R is false
4. A is false; R is true.