Statistics Test...

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:

No. of letters	No. of surnames
1-4	6
4-7	30
7-10	40
10-13	16
13-16	4
16-19	4

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

The following data gives the information on the observed lifetimes (in hours) of $$225$$ electrical components:

Lifetimes (in hours)	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	10	35	52	61	38	29

Determine the modal lifetimes of the components.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data.

No. of cars	Frequency
0-10	7
10-20	14
20-30	13
30-40	12
40-50	20
50-60	11
60-70	15
70-80	8

A life insurance agent found the following data for distribution of ages of $$100$$ policy holders. Calculate the median age, if policies are only given to person having age $$18$$ years onwards but less than $$60$$ years.

Age (in years)	No. of policy holders
Below $$20$$	$$2$$
Below $$25$$	$$6$$
Below $$30$$	$$24$$
Below $$35$$	$$45$$
Below $$40$$	$$78$$
Below $$45$$	$$89$$
Below $$50$$	$$92$$
Below $$55$$	$$98$$
Below $$60$$	$$100$$

If the median of the distribution given below is $$28.5$$. Find the values of $$x$$ and $$y$$.

Class interval	Frequency	Cumulative frequency
0-10	5	5
10-2	x	5+x
20-30	20	25+x
30-40	15	40+x
40-50	y	40+x+y
50-60	5	45+x+y
Total	60

Length (in mm)	No. of leaves
118-126	3
127-135	5
136-144	9
145-153	12
154-162	5
163-171	4
172-180	2

The length of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table. Find the median length of the leaves

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg)	No. of students
40-45	2
45-50	3
50-55	8
55-60	6
60-65	6
65-70	3
70-75	2

If the mode of a distribution is $$18$$  and the mean is $$ 24$$, then median is

The ages of $$40$$ students in a class are given. Find the mean age of the class

The following table shows the marks obtained by 100 students of class x in a school during a particular academic session. Find the mode of this distribution.

Marks	No. of students
Less than 10	7
Less than 20	21
Less than 30	34
Less than 40	46
Less than 50	66
Less than 60	77
Less than 70	92
Less than 80	100