Frank solutions for Mathematics [English] Class 9 ICSE chapter 22 - Statistics [Latest edition]

Define primary data and secondary data.

Explain the meaning of the following terms: Variate

Explain the meaning of the following terms: Class mark

Explain the meaning of the following terms: True Class Limits

Explain the meaning of the following terms: Frequency

The mark obtained by the students in a class test are given below: 
31, 12, 28, 45, 32, 16, 49, 12, 18, 26, 34, 39, 29, 28, 25, 46, 32, 13, 14, 26, 25, 34, 23, 23, 25, 45, 33, 22, 18, 37, 26, 19, 20, 30, 28, 38, 42, 21, 36, 19, 20, 40, 48, 15, 46, 26, 23, 33, 47, 40.

Arrange the above marks in classes each with a class size of 5 and answer the following:
(i) what is the highest score?
(ii) What is the lowest score?
(iii) What is the range?
(iv) If the pass mark is 20, how many students failed/
(v) How many students got 40 or more marks?

The runs scored by a cricket player in the last 30 innings are:

75, 125, 36, 89, 154, 56, 12, 28, 96, 142, 78, 54, 30, 88, 116, 104, 55, 84, 10, 29, 31, 08, 24, 136, 117, 22, 99, 80, 112, 35.

Arrange these scores in an ascending order and answer the following:

1. Find the highest score.
2. Find the number of centuries scored by him.
3. Find the number of times he scored over 50.
4. Find the number of times he failed to score a 50.

Find the class boundaries and class marks of the following classes:
55 - 59, 60 - 64, 65 - 69, 70 - 74, 75 - 79, 80 - 84, 85 - 89, 90 - 94 and 95 - 99.

Find the actual (or true) lower and upper class limits and class-marks (or mid values) of the following classes: 2.1 - 4.0, 4.1 - 6.0 and 6.1 - 8.0.

Observe the given frequency table to answer the following:

a. The true class limits of the fifth class.
b. The size of the second class.
c. The class boundaries of the fourth class.
d. The upper and lower limits of the sixth class.
e. The class mark of the third class.

The number of goals scored by Arsenal Football Club in the English Premier League in the season 2007 were:
1, 2, 1, 3, 2, 5, 1, 6, 4, 4, 2, 3, 5, 6, 4, 2, 2, 3, 4, 1, 0, 5, 0, 5, 3, 2, 3, 4, 4, 1, 1, 2, 4, 3. 1. 4
Arrange these data in a distance frequency distribution table and answer the following:
(i) What is the range of the number of goals scored by AFC?
(ii) How many times did AFC score 3 or more than 3 goals?
(iii) Which variatie has the highest frequency?

If the class intervals of a frequency distribution are 5 - 12, 13 - 20, 21 - 28, 29 - 36, 37 - 44, 45 - 52 and 53 - 60, find the following:
(i) The class limits and class boundaries of 21 - 28
(ii) The class size and the class mark of the class interval 45 - 52.
(iii) Find the true class limits of all the class intervals.

The class marks of a frequency distribution are: 15, 25, 35, 45, 55, 65 and 75. Determine the class limits.

The class marks of a frequency distribution are: 27, 32, 37, 42, 47, 52, 57, 62, 67, 72 and 77. Find the class size and true class limits.

Construct a grouped frequency table from the following data of the daily wages earned by 60 labourers in a company. Take each class size as 7.

25, 26, 34, 48, 39, 16, 55, 28, 37, 42, 45, 55, 28, 54, 53, 18, 35, 47, 44, 28, 55, 45, 39, 54, 21, 49, 45, 38, 29, 53, 48, 44, 15, 28, 14, 32, 15, 44, 14, 15, 16, 41, 33, 52, 29, 34, 51, 22, 19, 37, 44, 25, 48, 38, 24, 52, 51, 42, 32, 27.

Prepare a cumulative frequency distribution table of the marks scored by 60 students in a test are given below:

The table given below shows the ages of patients being treated in a hospital. Construct a cumulative frequency distribution table for the same:

The electricity bills of 45 houses in a particular locality are given below. Tabulate the given data and present it as a cumulative frequency table with one of the classes being 300 - 450:
784, 567, 890, 231, 150, 458, 356, 762, 386, 824, 525, 663, 724, 841, 315, 641, 156, 715, 156, 317, 814, 547, 879, 456, 463, 664, 175, 584, 515, 487, 871, 511, 522, 454, 247, 819, 412, 326, 445, 311, 321, 545, 344, 266, 351.

From the cumulative frequency distribution given below, construct a frequency distribution table:

Construct a frequency distribution table from the given cumulative frequency distribution showing the weights of 750 students in a school:

a. Find the number of students whose weight lie in the interval 40-45
b. Find the interval which has the most number of students.

For the set of numbers given below, find mean: 5, 7, 8, 4, 6

For the set of numbers given below, find mean: 3, 0, 5, 2, 6, 2

Calculate man of the following: 4, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 11, 3

The weight of the seven members of a family, in kilograms are given below:
20, 52, 56, 72, 64, 13, 80.
Find mean weight.

A boy scored the following marks in various class tests during a terminal exam, each test being marked out of 20.
17, 15, 16, 7, 10, 14, 12, 19, 16, 12
Find his average mean marks.

Individual scores of a school cricket eleven in a match are given below:
10, 9, 31, 45, 0, 4, 8, 15, 12, 0, 6
Find the average score.

The daily maximum relative humidity (in percent) in Mumbai from May 1 to May 7, 1992 is given below: 64, 70, 65, 80, 75, 78
Find the mean.

The marks obtained by 10 students are listed below:
2, 5, 3, 8, 0, 9, x, 6, 1, 8
If the mean marks is 5, find x.

The height of 8 students X in centimetres are given below:
148, 162, 160, 154, 170, 162, x, 152
If the mean height is 158, find x.

If the mean of 7, 16, 9, 15, 16, a, 12, 8, b, 11 is 12, write a in terms of b.

A test  out of 25 marks was given to 16 students and marks scored are recorded below:
25, 8, 14, 20, 16, 22, 10, 15, 8, 7, 24, 18, 19, 6, 11, 14
Find the mean marks

A test out of 25 marks was given to 16 students and marks scored are recorded below: 25, 8, 14, 20, 16, 22, 10, 15, 8, 7, 24, 18, 19, 6, 11, 14
In the report, marks were entered out of 50. What is the mean of the recorded marks in the report?

In History project, marks out of 20 were awarded to 8 students. The marks were as shown below:
14, 16, 18, 14, 16, 14, 12, 16
Find the mean marks.

In History project, marks out of 20 were awarded to 8 students. The marks were as shown below: 14, 16, 18, 14, 16, 14, 12, 16
Each of the above students was 2 extra marks for submitting the project a week before the due date. What is the revised mean of this group?

The mean of 16 natural numbers is 48. Find the resulting mean, if each of the number is  increased by 5

The mean of 16 natural numbers is 48. Find the resulting mean, if each of the number is decreased by 8

The mean of 16 natural numbers is 48. Find the resulting mean, if each of the number is multiplied by 4

The mean of 16 natural numbers is 48. Find the resulting mean, if each of the number is divided by 0.25

The mean of 16 natural numbers is 48. Find the resulting mean, if each of the number is increased by 50%

The mean of 16 natural numbers is 48. Find the resulting mean, if each of the number is decreased by 10%

The mean of 4 observations is 20. If one observation is excluded, the mean of the remaining observations becomes 15. Find the excluded observation.

The mean monthly income of 8 men is Rs. 8079.75. A man whose monthly income is Rs. 8280 has also been taken into consideration. Calculate the mean monthly income of all the men.

The mean of 200 observations is 20. It is found that the value of 180 is wrongly copied as 280. Find the actual mean.

Find the median of the following sets of numbers.
15, 8, 14, 20, 13, 12, 16

Find the median of the following sets of numbers.
25, 11, 15, 10, 17, 6, 5, 12.

Calculate the median of the following sets of number:
1, 9, 10, 8, 2, 4, 4, 3, 9, 1, 5, 6, 2 and 4.

3, 8, 10, x, 14, 16, 18, 20 are in the ascending order and their median is 13. Calculate the numerical value of x.

The following data has been arranged in ascending order.
0, 1, 2, 3, x + 1, x + 5, 20, 21, 26, 29.
Find the value of x, if the median is 5.

A boy scored the following marks in various class tests during a term, each test being marked out of 20.
15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16
What is his mean marks?

A boy scored the following marks in various class tests during a term, each test being marked out of 20.
15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16
What is his median marks?