Direct Method of Finding Mean

Q.

If $x_i$ are the mid-points of the class intervals of grouped data, $f_i$ are the corresponding frequencies and $\overline{x}$ is the mean, then $\sum f_i(x_i-\overline{x})$ is equal to ____.

1. 2

2. -1

3. 1

4. 0

Q. The number of members in the 40 families in Bhilar are as follows:
1, 6, 5, 4, 3, 2, 7, 2, 3, 4, 5, 6, 4, 6, 2, 3, 2, 1, 4, 5, 6, 7, 3, 4, 5, 2, 4, 3, 2, 3, 5, 5, 4, 6, 2, 3, 5, 6, 4, 2. Prepare a frequency table and find the mean of members of 40 families.

Q.

The number of Science and Mathematics projects submitted by Model high school, Nandpur in last $20$ years at the state level science exhibition is:

$2,3,4,1,2,3,1,5,4,2,3,1,3,5,4,3,2,2,3,2$.

Prepare a frequency table and find the mean of the data.

Q.

If the class interval are $10-19,20-29,30-39,.....$, then the upper limit of the first class interval will be

1. $19$

2. $19.5$

3. $20$

4. $20.5$

Q. The following table shows the electricity (in units) used by 25 families of Eklara village in a month of May. Complete the table and answer the following questions.

Electricity used (units) xi	No. of Families (frequency) fi	fi×xi
30	7	.......
45	2	.......
60	8	.......
75	5	.......
90	3	.......
	N = .......	∑fixi =.......

(1) How many families use 45 units electricity?
(2) State the score, the frequency of which is 5.
(3) Find N, and ∑f_ix_i
(4) Find the mean of electricity used by each family in the month of May.

Q.

Find the mean age in years from the frequency distribution given below:
$\begin{array}{cc}Classintervalofageinyears& Frequency\left(f_i\right)\\ 25-30& 4\\ 30-35& 14\\ 35-40& 22\\ 40-45& 16\\ 45-50& 6\\ 50-55& 5\\ 55-60& 3\\ Total& 70\end{array}$

1. 39.85

2. 39.40

3. 40.15

4. 40.39

Q. Five years hence, the edge of Jacob will be three times that of his son. Five years ago, Jacob's edge was seven times that of his son. What are their present ages .

Q.

Using the aasumed - mean method, find the mean height of the plants from the following frequency-distribution table:

$\begin{array}{cccccc}\text{Height (in cm)}{x}_i& 60& 64& 68& 72& 76\\ \text{Number of plants}{f}_i& 5& 16& 40& 30& 9\end{array}$
[4 MARKS]

Q.

Find the mean of the given data.

$\begin{array}{cc}Classinterval& Frequency\\ 0-100& 7\\ 100-200& 11\\ 200-300& 15\\ 300-400& 9\\ 400-500& 8\end{array}$ [3 MARKS]

Q. Difference between the face values of $9$ and $5$ in $842,928$ & $165,234$ is

Q. The following histogram shows the number of literate females in the age group of $10$ to $40$ years in a town:
In which age group literate females are the least?

Q. If the mean of the following frequency distribution is $7$, find the value of $p$.

variables	2	3	5	10	13
Frequency	4	8	p	12	6

Q. John, received the given graph as the record of his heart rate. If the average heart rate of a healthy person is 72 beats per minute. Calculate John's health using the given formula.
(The formula can only be used for average heart rates less than 72.)

$Health=\frac{\text{Average heart rate}}{72}\times 100$

1. 65%
2. 54%
3. 90%
4. 75%

Q.

The double bar graph given shows the points scored
by three players in a game. What is the difference in player P’s score this year from player Q’s score last year?

A) 0
B) 100
C) 150
D) 200

Q. If the mean of the following frequency distribution is $8$, find the value of $k$.

x	2	4	6	8	10	12
f	4	7	10	16	k	3

Q. A survey was conducted by a group of students as a part of their environment awareness programme, 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.

Number of Plants	0-2	2-4	4-6	6-8	8-10	10-12	12-14
Number of houses	1	2	1	5	6	2	3

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

1. None of these
2. $8.2$ plants
3. $6.5$ plants
4. $5.7$ plants