Direct Method of Finding Mean

Q.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days	0 − 6	6 − 10	10 − 14	14 − 20	20 − 28	28 − 38	38 − 40
Number of students	11	10	7	4	4	3	1

Q.

Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is $50$.

$\begin{array}{cc}{x}_i& f_i\\ 10& 17\\ 30& f_1\\ 50& 32\\ 70& f_2\\ 90& 19\\ \text{Total}& 120\end{array}$

Q.

The mean of the following data is 42. Find the missing frequencies x and y if the sum of frequencies is 100.
$\begin{array}{ccccccccc}\text{Class interval}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 7& 10& x& 13& y& 10& 14& 9\end{array}$

Q.

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency $f_1$ and $f_2$
Class: 0-20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120
Frequency: 5 $f_1$ 10 $f_2$ 7 8

Q. The variance of the data 2, 4, 6, 8, 10 is:

1. 7
2. 8
3. 6
4. none of these

Q.

If the mean of the following frequency distribution is 54, find the value of p.
$\begin{array}{cccccc}\text{Class}& 0-20& 20-40& 40-60& 60-80& 80-100\\ \text{Frequency}& 7& p& 10& 9& 13\end{array}$

Q.

The daily expenditure of 100 families are given below. Calculate $f_1$ and $f_2$ if the mean daily expenditure is Rs. 188.
$\begin{array}{cccccc}\text{Expenditure (in Rs.)}& 140-160& 160-180& 180-200& 200-220& 220-240\\ \text{Number of}& & & & & \\ \text{families}& 5& 25& f_1& f_2& 5\end{array}$

Q.

Question 1(c)

Estimate the following using general rule:
12, 904 + 2, 888

Q.

A student noted the number of cars passing throught a spot on a road for 100 periods each of 3 minutes and summarized it in the table gives below.

The mode, median and mean of the data is

1. Mean = 45.6, mode = 47.7, median = 4

2. Mean = 40.6, mode = 44.7, median = 42

3. Mean = 42.6, mode = 43.7, median = 46

4. Mean = 42.6, mode = 34.7, median = 32

Q.

Find the mean of the following data, using direct method:
$\begin{array}{ccccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequency}& 7& 5& 6& 12& 8& 2\end{array}$

Q. The mean of the following frequency distribution is 41. The value of a is equal to

$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 0-20& 12\\ 20-40& 8\\ 40-60& a\\ 60-80& 6\\ 80-100& 4\end{array}$

1. 18
2. 10
3. 15
4. 9

Q. The mean of the following frequency distribution is 50. Find the value of p.

Classes	0−20	20−40	40−60	60−80	80−100
Frequency	17	28	32	p	19

Q. The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:

Marks (x):	15	20	22	24	25	30	33	38	45
Frequency (f):	5	8	11	20	23	18	13	3	1

Find the average number of marks.

Q. Must the class intervals be continuous for mean, median, mode?

Q.

A survey was conducted by a group of students as a part of their environment awareness program, in which they collected the following data regarding the number of plants in $20$ houses in a locality. Find the mean number of plants per house.

$\begin{array}{cccccccc}\text{Number of plants}& 0-2& 2-4& 4-6& 6-8& 8-10& 10-12& 12-14\\ \text{Number of Houses}& 1& 2& 1& 5& 6& 2& 3\end{array}$

Which method did you use for finding the mean, and why?

Q.

Calculate the average daily income of the following data about men working in a company

Daily income <100. < 200 <300. <400. <500

No. Of men. 12. 28. 34. 41. 50

Q. Question 6
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
$\begin{array}{ccccccc}Numberofletters& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ Numberofsurnames& 6& 30& 40& 6& 4& 4\end{array}$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

Q.

The average of the first five multiples of 5 is ___.

Q. The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals are given in the following frequency table:

No. of calls (x):	0	1	2	3	4	5	6
No. of intervals (f):	15	24	29	49	54	43	39

Compute the mean number of calls per intervals.

Q.

The following table gives, the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method. $\begin{array}{cccccc}\text{Literacy rate(\%)}& 45-55& 55-65& 65-75& 75-85& 85-95\\ \text{Number of cities}& 4& 11& 12& 9& 4\end{array}$

Q. Can we use assumed mean method to find the mean of grouped data when its class interval are irregular.If not why?

Q. If the mean of first n natural number is 15, then n =

(a) 15
(b) 30
(c) 14
(d) 29

Q.

Question 91

The population of a town was decreasing every year due to migration, poverty and unemployment. The present population of the town is 631680. Last year the migration was 4% and the year before last, it was 6%. What was the population two years ago ?

Q.

Find the mean of the first ten odd natural numbers?

Q. If the mean of 3, 4, x, 7, 10 is 6, then the value of x is 5.

1. 4
2. 5

Q.

Below Given Are The Daily Wages Of $110$ Workers, Obtained In A Survey. Compute The Mean Daily Wages And Modal Daily Wages Of These Workers.

$=18$

Q.

The contents of 100 match boxes were checked to determine the number of matches they contained.

Calculate correct to one decimal place the mean number of matches per box; determine how many extra matches would be needed to be added to the total contents of the $100$ boxes to bring the mean to exactly $39$.

1. $35.1,86$

2. $38.1,86$

3. $36.1,88$

4. $36.1,90$

5. $38.1,87$

Q. The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of number of boys to the number of girls who appeared in the examination.

Q. If the mean of the following distribution is 27, find the value of p.

Class:	0−10	10−20	20−30	30−40	40−50
Frequency:	8	p	12	13	10

Q. Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss	No. of tosses
0 1 2 3 4 5	38 144 342 287 164 25
Total	1000