Mean of Discrete Series

Q.

Calculate arithmetic mean using direct method.

$\begin{array}{cccccc}\text{Wages (in Rs)}& 10& 20& 30& 40& 50\\ \text{Number of workers}& 4& 5& 3& 2& 1\end{array}$

Q.

Following information pertains to the daily income of 150 families. Calculate the arithmetic mean.

$\begin{array}{cc}\text{Income (in Rs)}& \text{Number of Families}\\ \text{More than 75}& 150\\ \text{More than 85}& 140\\ \text{More than 95}& 115\\ \text{More than 105}& 95\\ \text{More than 115}& 70\\ \text{More than 125}& 60\\ \text{More than 135}& 40\\ \text{More than 145}& 25\end{array}$

Q.

The following table gives the daily income of ten workers in a factory. Find the arithmetic mean.

$\begin{array}{ccccccccccc}\text{Workers}& A& B& C& D& E& F& G& H& I& J\\ \text{Daily Income (in Rs)}& 120& 150& 180& 200& 250& 300& 220& 350& 370& 260\end{array}$

Q.

Find the mean daily wages of $60$ workers in a factory as per the data given below:

Daily wages ( in rupees)	$90$	$110$	$120$	$130$	$150$
Number of workers	$12$	$14$	$13$	$11$	$10$

Q.

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

1. ^ΣF_ix_i ⁄_ΣFi

2. ^ΣF_i ⁄_Xi

3. ^ΣX_i ⁄_Fi

4. ^ΣF_ix_i ⁄_ΣX.F

Q. [dummy] The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
$\begin{array}{cc}\text{Literacy rate (in \%)}& \text{No. of cities}\\ 44-55& 3\\ 55-65& 10\\ 65-75& 11\\ 75-85& 8\\ 85-95& 3\end{array}$

1. 66.44
2. 67.39
3. 71.55
4. 69.43

Q. The hourly wages of 30 workers are given below. Find the mean wage using the assumed mean method.
$\begin{array}{cc}Wage\left(inRs\right)& Numberofworkers\\ 10& 6\\ 20& 8\\ 30& 9\\ 40& 4\\ 50& 3\end{array}$

1. Rs 18
2. None of these
3. Rs 26.66
4. Rs 30

Q. [dummy] The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
$\begin{array}{cc}\text{Literacy rate (in \%)}& \text{No. of cities}\\ 44-55& 3\\ 55-65& 10\\ 65-75& 11\\ 75-85& 8\\ 85-95& 3\end{array}$

1. 66.44
2. 69.43
3. 67.39
4. 71.55

Q. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate by step deviation method.
$\begin{array}{cc}\text{Literacy rate (in \%)}& \text{No. of cities}\\ 45-55& 3\\ 55-65& 10\\ 65-75& 11\\ 75-85& 8\\ 85-95& 3\end{array}$

1. 69.43
2. 67.39
3. 71.55
4. 66.44

Q.

Calculate the weighted mean of the following distribution.

$\begin{array}{ccccc}\text{Items}& 12& 29& 14& 41\\ \text{Weight}& 6& 4& 5& 2\end{array}$

Q.

For a distribution,
$\sum FX=5x+2,\sum F=12$

If the mean of the distribution is 6, what is the value of x?

1. 12

2. 15

3. 14

4. 18

Q.

If the mean of the following data is 17 then the value of p is

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$$\begin{array}{cccccc}X& \text{10}& \text{p}& \text{18}& \text{21}& \text{25}\\ F& \text{10}& \text{15}& \text{7}& \text{9}& \text{9}\end{array}$$

Q. The distribution of height of 50 children is 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. None of these

Q.

The mean of the following distribution is
$$\begin{array}{ccccc}{x}_i& \text{10}& \text{13}& \text{16}& \text{19}\\ f_i& \text{2}& \text{5}& \text{7}& \text{6}\end{array}$$

1. 16

2. 15.2

3. 15.35

4. 15.55

Q.

For the following data, mean of x is found to be 7.3. The missing frequency is
x : 5 6 7 8 9
f : 4 6 12 - 8

1. 9

2. 7

3. 10

4. 8