Frequency Table & Its Average

Q. Question 2
Calculate the mean of the scores of 20 students in a mathematics test
$\begin{array}{cccccc}\text{Marks}& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of students}& 2& 4& 7& 6& 1\end{array}$

Q. Heights in cm of 12 students are given as:

154, 158, 155, 160, 165, 145, 148, 150, 147, 151, 166, 152

Make a frequency table taking 145-150 as first class interval.

Q.

If the mean of 6, 4, 7, x and 10 is 8, the value of x is

1. 13

2. 32

3. 90

4. 22

Q. The average of 'n' terms is zero. How many maximum numbers of terms can be negative?

1. n
2. 0
3. n + 1
4. n - 1

Q.

Find the average marks obtained by 20 students in a class.

$$\begin{array}{cc}Marks& Frequency\\ 87& 2\\ 78& 3\\ 53& 1\\ 98& 2\\ 92& 2\\ 97& 1\\ 81& 2\\ 65& 2\\ 98& 3\\ 76& 2\end{array}$$

1. 83.8

2. 83.4

3. 81.8

4. 82.8

Q.

If the mean of the following data is 17, then find the value of 'p'.

$\begin{array}{cccccc}{x}_i& \text{10}& \text{p}& \text{18}& \text{21}& \text{25}\\ f_i& \text{10}& \text{15}& \text{7}& \text{9}& \text{9}\end{array}$

1. 14

2. 15

3. 24

4. 16

Q.

The distribution of the heights of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table.
$\begin{array}{ccccccc}Height& 110& 115& x_1& 120& 121& 125\\ Numberofstudents& 6& 8& 14& f_1& 4& 3\end{array}$

1. $x_1=118,f_1=15$

2. $x_1=121,f_1=15$

3. $x_1=118,f_1=8$

4. $x_1=221,f_1=45$

Q.

Statistics is concerned with

1. Manipulation of data

2. Distribution of data

3. Drawing figures

4. Collection and Analyzation of data

Q.

For discontinuous grouped data, the class interval is given in _______ form.

1. inclusive

2. exclusive

3. class-mark

4. frequency

Q. The average of the first five multiples of 9 is:

1. 18
2. 27
3. 36
4. 45

Q.

The mean of the following distribution is ____.

$$\begin{array}{ccccc}{x}_i& 10& 13& 16& 19\\ f_i& 2& 5& 7& 6\end{array}$$

1. 15.55

2. 15.35

3. 16

4. 14.3

Q. Question 12
Find the unknown entries a, b, c, d, e and f in the following distribution of heights of students in a class
$\begin{array}{ccc}Height\left(incm\right)& Frequency& Cumulativefrequency\\ 150-155& 12& a\\ 155-160& b& 25\\ 160-165& 10& c\\ 165-170& d& 43\\ 170-175& e& 48\\ 175-180& 2& f\\ Total& 50& \end{array}$

Q. The histogram gives the information about the number of literate males along with their age. Below the age of 30, how many males are literate?

1. 900

Q.

The class marks of a frequency distribution are given as follows: 15, 20, 25, .................... The class corresponding to the class Mark 20 is?

Q.

If the class-marks of a frequency distribution are 10.5, 16.5, 22.5, 28.5, 34.5, then the class-size is

1. 6.5

2. 6

3. 5

4. 5.5

Q.

The marks obtained by the students of a class , in an exam which was out of 50 marks is given below :

$\begin{array}{cc}Marks& Numberofstudents\\ 5& 1\\ 7& 2\\ 11& 2\\ 16& 3\\ 21& 5\\ 24& 6\\ 28& 3\\ 32& 5\\ 34& 8\\ 39& 6\\ 43& 4\\ 45& 2\\ 49& 3\end{array}$

Find the mean for the ungrouped data.

1. 24
2. 28
3. 30.5
4. 29.94

Q.

If the observations 3, 5, 7, 4 have frequencies x, x+4, x-3, x+8 respectively and mean of these observations is 4, then find the value of 'x'.

1. $\frac{5}{3}$
2. $\frac{7}{4}$
3. $\frac{2}{3}$
4. $\frac{11}{3}$

Q.

Candidates of 5 schools appear for a Maths test. The data is given as follows :

$\begin{array}{ccc}\text{Schools}& \text{No.of Candidates}& \text{Score}\\ A& 60& 75\\ B& 48& 80\\ C& -& 55\\ D& 40& 50\\ E& 50& 60\end{array}$

If the average score of the candidates is 64.8, find the number of candidates who appeared from School C.

1. 52

2. 56

3. 60

4. 62

Q.

What do we understand by the term 'statistics'?

1. Collection and organistaion of data

2. Analysis of data

3. Interpretation of data

4. All of the above

Q. Explain, by taking a suitable example, how the arithmetic mean alters by (i) adding a constant k to each term, (ii) subtracting a constant k from each them, (iii) multiplying each term by a constant k and (iv) dividing each term by a non-zero constant k.

Q. Statistics helps us in drawing meaningful inferences from data collected in numerous experiments

1. True
2. False

Q. Find the mean of first five multiples of 3.

Q.

The following is a statistical question.

Did Shyam watch television last night?

1. True

2. False

Q.

Find the mean of the given data.

$\begin{array}{cc}Classinterval& Frequency\\ 0-100& 7\\ 100-200& 11\\ 200-300& 15\\ 300-400& 9\\ 400-500& 8\end{array}$

1. 240

2. 230

3. 250

4. 190

Q.

If a+b+c = 13, then what is the maximum value of

(a - 3)( b - 2)(c + 1)

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.

1. 434
2. 208
3. 444
4. Data inadequate

Q. Statistics helps us in drawing meaningful inferences from data collected in numerous experiments. State true or false.

1. True
2. False

Q.

The following table shows the marks obtained by 5 students in a class. Find the average marks of the class.

$$\begin{array}{cc}Marks& Frequency\\ 98& 1\\ 65& 1\\ 88& 2\\ 54& 1\end{array}$$

1. 76.6

2. 77.6

3. 78.6

4. 78.9

Q. In English exam, the average of Class $A$ was found to be $x$ marks. After deducting a computational error, the average marks of $100$ candidates got reduced from $74$ to $54$. The average thus came down by $25$ marks. The total numbers of candidates who took the English exam were?

Q.

Determine whether the following is a statistical question for data pertaining to internet searches.

How many internet searches do the residents at Jacque’s retirement home perform each day? (Yes/No)

__