Mean for Ungrouped Data

Q.

Which of the following measures of central tendency takes into account all the observations?

1. Mean

2. Median

3. Mode

4. All of the above

Q.

Sum of all observations divided by the number of observations gives us the_______ of the data.

Q. Question 1
Find the mean marks of students for the following distribution
$\begin{array}{cc}Marks& Numberofstudents\\ 0andabove& 80\\ 10andabove& 77\\ 20andabove& 72\\ 30andabove& 65\\ 40andabove& 55\\ 50andabove& 43\\ 60andabove& 28\\ 70andabove& 16\\ 80andabove& 10\\ 90andabove& 8\\ 100andabove& 0\end{array}$

Q.

The mean calculated for the raw data will have the exact same value as that of the corresponding grouped data.

1. True

2. False

Q.

$\begin{array}{cc}{x}_i& f_i\\ 4& 10\\ 8& 11\\ 12& 9\\ 16& 13\end{array}$
Find $\sum f_i{x}_i$ from the given table. $f$ = frequency

1. 444

2. Data inadequate

3. 434

4. 208

Q. If the mean of $x,x+3,x+5,x+7$ and $x+10$ is 9, then the value of second observation is ____.

1. 5
2. 6
3. 7
4. 8

Q. The measure of central tendency which we'll reject when the data contains some extreme values, is the _____.

1. mean
2. median
3. mode
4. range

Q. A die is thrown once. Find the probability of getting a number which
(i) a prime number; (ii) a number lying between $2$ and $6$;

Q. Let a, b, and c be positive integers($a<b<c$). If the average (arithmetic mean) of a, b, and c is $100$, which of the following is NOT a possible value of any of the integers?

1. $297$
2. $298$
3. $299$
4. $2$
5. $100$

Q. Find the mean age in years from the frequency distribution given below.
$\begin{array}{cc}Classintervalofageinyears& Frequency\left(f_i\right)\\ 25-29& 4\\ 30-34& 14\\ 35-39& 22\\ 40-44& 16\\ 45-49& 6\\ 50-54& 5\\ 55-59& 3\\ Total& 70\end{array}$

1. 39.35
2. 39.39
3. 40.15
4. 40.39

Q.

The mean of first 10 natural numbers is ______.

1. 4.5

2. 5.5

3. 6.5

4. 5

Q.

Krishna’s family has 4 members. The daily rice consumption of the 4 family members is - 0.5 kg, 0.4 kg, 0.3 kg and 0.6 kg. Krishna wants to find the average rice consumption per family member. What is the measure that will come into use now?

1. Median

2. Mean

3. Mode

4. Median or Mode

Q.

There are four children A, B, C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 10 chocolates. Which of these children has close to the average number of chocolates?

1. B

2. D

3. C

4. A

Q.

$\sum$fx = 5x + 2, $\sum$f = 12. If the mean of the distribution is 6, what is the value of x?

1. 12

2. 14

3. 15

4. 18

Q. The mean of $6$, $y$, $7$, $x$ and $14$ is $8$, then

1. $x+y=13$
2. $x-y=13$
3. $2x+3y=13$
4. $x^2+y^2=15$

Q.

Calculate the Mean of the given distribution, using Assumed mean Method.

$\begin{array}{cc}\text{Marks}& \text{No. of Students}\\ 10-20& 2\\ 20-30& 6\\ 30-40& 10\\ 40-50& 12\\ 50-60& 9\\ 60-70& 8\\ 70-80& 4\\ 80-90& 3\end{array}$

1. 48.89

Q. If the mean of $x$ and $\frac{1}{x}$ is M, the mean of $x^3$ and $\frac{1}{x^3}$ is _____.

1. $\frac{M^2-3}{2}$
2. $M(4M^2-3)$
3. $M^3$
4. $M^3+3$

Q.

The value of ${\sum }_{i=1}^n{x}_i$ is

1. $\frac{\overline{X}}{2}$

2. $\frac{\overline{X}}{n}$

3. $2\overline{X}$

4. $n\overline{X}$

Q.

The mean $\overline{x}$ of a grouped data is given by:

1. $\frac{\sum f_i{x}_i}{\sum f_i}$

2. $\frac{\sum f_i}{x_i}$

3. $\frac{\sum x_i}{f_i}$

4. $\frac{\sum f_i{x}_i}{\sum x.f}$

Q.

The average weight of a group of 25 men was calculated to be 78.4 kg. It was discovered later that one weight was wrongly entered as 69 kg instead of 96 kg. What is the correct average ?

1. 80.30

2. 79.48

3. 77.56

4. 75.76

Q. If the mean of the following distribution is 6, then value of p is
$x:24610p+5$
$f:32312$

1. $5$
2. $7$
3. $6$
4. $12$

Q.

The arithmetic mean of 1, 2, 3, 4, 5, ……., n is ____.

1. $\frac{n+1}{2}$

2. $\frac{n-1}{2}$

3. $\frac{n}{2}$

4. $\frac{n}{2}+1$

Q. The three methods to find the mean from the grouped frequency distribution are _______.

1. Assumed method, Direct mean method and Step deviation method
2. Direct method, Assumed mean method and Step deviation method
3. Grouped method, Ungrouped method and Step deviation method.
4. Grouped method, Ungrouped method and Direct method.

Q. There are _______ methods to find the mean value for a grouped data.

1. two
2. three
3. four
4. five

Q. The following are the marks obtained in Maths by students of Class 8:
51, 94, 34, 20, 50, 81, 81, 90, 76, 34, 51, 86, 93, 99, 26, 54, 85, 71, 88, 40, 44, 56, 55, 57, 78, 53, 81, 78, 65, 78.
The data have to be grouped to find the mean marks.
One of the class intervals made is 60-70.
How many should such class intervals be prepared?
What is the frequency of the last class interval?
What are the upper and the lower limits of the first class interval?
What is $\sum f_i$ ?

1. 8, 4, 30, 20, 30
2. 10, 1, 0, 10, 30
3. 10, 4, 10, 0, 30
4. 8, 4, 20, 30, 28

Q.

What is the ratio of the sum of all observations to the number of observations called?

__

Q.

The mean of marks scored by $100$ students was found to be $40$. Later on, it was discovered that a score of $53$ was misread as $83$. Find the correct mean.

Q. The frequency of an entry is the number of times the entry occurs in the dataset.

1. False
2. True

Q.

The mean calculated for the raw data will have the exact same value as that of the corresponding grouped data.

1. True

2. False

Q. Find the class marks of classes 10−25 and 35−55.