Direct Method

Q.

Comment whether the following statements are true or false.

(i) The sum of deviation of items from median is zero.

(ii) An average alone is not enough to compare series.

(iii) Arithmetic mean is a positional value.

(iv) Upper quartile is the lowest value of top 25% of items.

(v) Median is unduly affected by extreme observations.

Q.

The mean of the series $x_1,x_2,x_3,.......,x_n$ is $\overline{x}$. If $x_2$ is replaced by $\lambda$, then the new mean is

1. $\frac{\overline{x}-x_2-\lambda }{n}$

2. $\overline{x}-x_2+\lambda$

3. $\frac{(n-1)\overline{x}+\lambda }{n}$

4. $\frac{n\overline{x}-x_2+\lambda }{n}$

Q. The mean marks of 100 students were found to be 40. Later on, it was discovered that a score of 53 was misread as 83. Then, the correct mean will be:

1. 38.7
2. 37.5
3. 35.6
4. 39.7

Q. The algebraic sum of the deviations of a frequency distribution from its mean is :

1. Always positive
2. Always negative
3. Non – zero number
4. 0

Q.

A person recorded the speed (in km/hr) of 10 motorists as 48, 52, 57, 55, 45, 39, 61, 49, 51 and 43. The average speed of the motorists is _____.

1. 57 km/hr

2. 50 km/hr

3. 55 km/hr

4. 54 km/hr

Q. A person recorded the speed (in km/hr) of 10 motorists as 48, 52, 57, 55, 45, 39, 61, 49, 51 and 43. The average speed of the motorists is .

1. 57 km/hr
2. 50 km/hr
3. 55 km/hr
4. 54 km/hr

Q. Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is

1. 48
2. 50
3. 80
4. 82 $\frac{1}{2}$

Q. The mean of a set of numbers is $\overline{x}.$ If each number is decreased by $\lambda ,$ the mean of the new set is

1. $\overline{x}$
2. $\overline{x}+\lambda$
3. $\lambda -\overline{x}$
4. $\overline{x}-\lambda$

Q.

The maximum temperature for the first ten days of July, $2006$ in a certain city were:

$43,44,42,41,36,43,42,40$

Calculate mean of the above data.

Q. Each observation in a raw data is first multiplied by 3, then 6 is added. It is then divided by 3 and subsequently reduced by 6. Which of the following statements is true?

1. The new mean is 4 more than the original mean
2. The new mean is equal to the original mean
3. The new mean is 4 less than the original mean
4. The new mean is 2 more than the original mean