Finding Mean for Grouped Data When Class Intervals Are Given

Q.

Question 8
The mean of the following frequency distribution is 50 but the frequencies $f_1$ and $f_2$ in classes 20-40 and 60-80, respectively are not known. Find these frequencies, if the sum of all the frequencies is 120.
$\begin{array}{cccccc}Class& 0-20& 20-40& 40-60& 60-80& 80-100\\ Frequency& 17& f_1& 32& f_2& 19\end{array}$

Q. Find the mean of each of the following frequency distributions :

Classes:	25−29	30−34	35−39	40−44	45−49	50−54	55−59
Frequency:	14	22	16	6	5	3	4

Q. If the mean of frequency distribution is 8.1 and Σf_ix_i = 132 + 5k, Σf_i = 20, then k =

(a) 3
(b) 4
(c) 5
(d) 6

Q. Question 1
In the formula $\overline{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$, for finding the mean of grouped data $d_i^{\prime }s$ are deviation from a of
(a) lower limits of the classes
(b) upper limits of the classes
(c) mid-points of the classes
(d) frequencies of the class marks

Q. For the following distribution, calculate mean using all suitable methods:

Size of item:	1−4	4−9	9−16	16−27
Frequency:	6	12	26	20

Q. Find the mean of each of the following frequency distributions :

Class interval:	0−6	6−12	12−18	18−24	24−30
Frequency:	7	5	10	12	6

Q. Find the mean of each of the following frequency distributions :

Class interval:	0−8	8−16	16−24	24−32	32−40
Frequency:	5	9	10	8	8

Q. The mean of a discrete frequency distribution x_i / f_i, i = 1, 2, ......, n is given by

(a) $\frac{\mathrm{\Sigma }{f}_i{x}_i}{\mathrm{\Sigma }{f}_i}$
(b) $\frac{1}{n}\sum _{i=1}^n{f}_i{x}_i$
(c) $\frac{{\displaystyle \sum _{i=1}^n}{f}_i{x}_i}{{\displaystyle \sum _{i=1}^n}{x}_i}$
(d) $\frac{{\displaystyle \sum _{i=1}^n}{f}_i{x}_i}{{\displaystyle \sum _{1=1}^n}i}$

Q.

While computing the mean of the grouped data, we assume that the frequencies are:

(a) evenly distributed over the classes

(b) centred at the class marks of the classes

(c) centred at the lower limits of the classes

(d) centred at the upper limits of the classes

Q. The mean obtained by all the three methods is not the same.

1. False
2. True

Q. Find the mean of each of the following frequency distributions :

Class interval:	0−8	8−16	16−24	24−32	32−40
Frequency:	5	6	4	3	2

Q. The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency f₁ and f₂.

Class:	0−20	20−40	40−60	60−80	80−100	100−120
Frequency:	5	f1	10	f2	7	9

Q. Find the missing frequencies f₁ and f₂ in the table in given below, it is being given that the mean of the given frequency distribution is 50.

Class	0-20	20-40	40-60	60-80	80-100	Total
Frequency	17	f1	32	f2	19	120

Q. Find the mean of each of the following frequency distributions :

Class interval:	25−35	35−45	45−55	55−65	65−75
Frequency:	6	10	8	12	4

Q. Using an appropriate method, find the mean of following frequency distribution:

Class interval	84−90	90−96	96−102	102−108	108−114	114−120
Frequency	8	10	16	23	12	11

Which method did you use, and why?

Q.

Question 6
The table below shows the daily expenditure on food of 25 households in a locality.

$\begin{array}{cccccc}\text{Daily expenditure (in Rs)}& 100-150& 150-200& 200-250& 250-300& 300-350\\ \text{Number of households}& 4& 5& 12& 2& 2\end{array}$

Find the mean daily expenditure on food by a suitable method.

Q.

Question 2
Consider the following distribution of daily wages of 50 worker of a factory.

$\begin{array}{cccccc}\text{Daily wages (in Rs)}& 100-120& 120-140& 140-160& 160-180& 180-200\\ \text{Number of workers}& 12& 14& 8& 6& 10\end{array}$

Find the mean daily wages of the workers of the factory by using an appropriate method.

Q.

Find the mean of the following frequency distribution:

1. 143

2. 147

3. 150

4. 146

5. 145

Q.

If there are two class intervals 10-20 and 20-30, then in which interval will 20 fall?

1. Neither in 10-20 nor 20-30

2. In both, 10-20 and 20-30

3. 20-30

4. 10-20

Q. If the arithmetic mean of the following frequency distribution is 57.6 and the sum of the observations is 50, then the missing frequencies x and y are

Classes	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	7	x	12	7	y	5

1. $x=10,y=8$
2. $x=8,y=10$
3. $x=9,y=10$
4. $x=10,y=9$

Q. If the range of discrete data of n observations is zero, then:

1. all values of data are equal to standard deviation
2. all values of data are equal
3. the extreme values of data are different
4. all values of data are zero

Q.

What is meant by standard error?

Q.

$if{x}_i^{\prime }sarethemidpointsoftheclassintervalsofagroupeddata,f_i^{\prime }sarethecorrespondingfrequenciesand\overline{x}isthemeanthen\sum f_i(x_i-\overline{x})=?$

(a) 1 (b) 0 (c) -1 (d) 2

Q. Find the mean of each of the following frequency distributions :

Class interval:	0-6	6-12	12-18	18-24	24-30
Frequency:	6	8	10	9	7

Q. Find the mean of each of the following frequency distributions :

Class interval:	0−8	8−16	16−24	24−32	32−40
Frequency:	6	7	10	8	9

Q. Find the upper class interval and match the following.

1. 100
2. 50
3. 200
4. 150

Q. The following table shows the frequency distribution of the diameters of 40 bottles. (Lengths have been measured to the nearest millimeter). Find the mean diameter.
$\begin{array}{cc}Diameter\left(mm\right)& Frequency\\ 35-39& 6\\ 40-44& 12\\ 45-49& 15\\ 50-54& 10\\ 55-60& 7\end{array}$

1. 45
2. 30
3. 47
4. 50

Q. In the formula $\overline{\mathrm{X}}=a+h\left(\frac{1}{N}\Sigma f_i{u}_i\right)$ , for finding the mean of grouped frequency distribution $u_i$ =
(a) $\frac{x_i+a}{h}$ (b) $h\left(x_i-a\right)$ (c) $\frac{x_i-a}{h}$ (d) $\frac{a-x_i}{h}$

Q. Find the mean, using assumed-mean method:

Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	20	35	52	44	38	31

Q. Find the mean age from the following frequency distribution:

Age (in years)	25-29	30-34	35-39	40-44	45-49	50-54	55-59
No. of person	4	14	22	16	6	5	3