RD Sharma solutions for Mathematics [English] Class 9 chapter 22 - Tabular Representation of Statistical Data [Latest edition]

What do you understand by the word “statistics” in
(i) Singular form
(ii) Plural form?

Describe some fundamental characteristics of statistics.

What is primary data?

What secondary data?

Which of the two – the primary or the secondary data – is more reliable and why?

Why do we group data?

Explain the meaning of the term Variable.

Explain the meaning of the term Class-integral.

Explain the meaning of the term Class-size.

Explain the meaning of the term Class-mark.

Explain the meaning of the term Frequency.

Explain the meaning of the term Class limits.

Explain the meaning of the term True class limits.

The ages of ten students of a group are given below. The ages have been recorded in years
and months:
8 – 6, 9 – 0, 8 – 4, 9 – 3, 7 – 8, 8 – 11,8 – 7, 9 – 2, 7 – 10, 8 – 8
(i) What is the lowest age?
(ii) What is the highest age?
(iii) Determine the range?

The monthly pocket money of six friends is given below: Rs. 45, Rs. 30, Rs. 40, Rs. 50, Rs.
25, Rs. 45.
(i) What is the highest pocket money?
(ii) What is the lowest pocket money?
(iii) What is the range?
(iv) Arrange the amounts of pocket money in ascending order.

Write the class-size in each of the following:
(i) 0 – 4, 5 – 9, 10 – 14
(ii) 10 – 19, 20 – 29, 30 – 39
(iii) 100 – 120, 120 – 140, 160 – 180
(iv) 0 – 0.25, 0.25 – 0.50, 0.50 – 0.75
(v) 5 – 5.01, 5.01 − 5.02, 5.02 – 5.03

The final marks in mathematics of 30 students are as follows:
53, 61, 48, 60, 78, 68, 55, 100,67,90
75,88,77,37,84,58,60,48,62,56
44, 58, 52, 64, 98, 59, 70, 39, 50, 60
(i) Arrange these marks in the ascending order, 30 to 39 one group, 40 to 49 second group etc.
Now answer the following:
(ii) What is the highest score?
(iii) What is the lowest score?
(iv) What is the range?
(v) If 40 is the pass mark how many have failed?
(vi) How many have scored 75 or more?
(vii) Which observations between 50 and 60 have not actually appeared?
(viii) How many have scored less than 50?

The weights of new born babies (in kg) in a hospital on a particular day are as follows:
2.3, 2.2, 2.1, 2.7, 2.6, 3.0, 2.5, 2.9, 2.8, 3.1, 2.5, 2.8, 2.7, 2.9, 2.4
(i) Rearrange the weights in descending order.
(ii) Determine the highest weight.
(iii) Determine the lowest weight.
(iv) Determine the range.
(v) How many babies were born on that day?
(vi) How many babies weigh below 2.5 kg?
(vii) How many babies weigh more than 2.8 kg?
(viii) How many babies weigh 2.8 kg?

The number of runs scored by a cricket. player in 25 innings are as follows:
26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 1.5, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64,47.
(i) Rearrange these runs in ascending order.
(ii) Determine the player, is highest score.
(iii) How many times did the player not score a run?
(iv) How many centuries did he score?
(v) How many times did he score more than 50 runs?

The class size of a distribution is 25 and the first class-interval is 200-224. There are seven
class-intervals.
(i) Write the class-intervals.
(ii) Write the class-marks of each interval.

Write the class size and class limits in each of the following:
(i) 104, 114, 124, 134, 144, 154, and 164
(ii) 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97 and 102
(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5

Following data gives the number of children in 40 families:
1,2,6,5,1,5, 1,3,2,6,2,3,4,2,0,0,4,4,3,2,2,0,0,1,2,2,4,3, 2,1,0,5,1,2,4,3,4,1,6,2,2.
Represent it in the form of a frequency distribution.

The marks scored by 40 students of class IX in mathematics are given below:
81, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70,
83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.
Prepare a frequency distribution with class size of 10 marks.

The heights (in cm) of 30 students of class IX are given below:
155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153

Prepare a frequency distribution table with 160-164 as one of the class intervals.

The monthly wages of 30 workers in a factory are given below:
83.0, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808,
812, 840, 885, 835, 836, 878, 840, 868, 890, 806, 840, 890.
Represent the data in the form of a frequency distribution with class size 10.

The daily maximum temperatures (in degree celsius) recorded in a certain city during the
month of November are as follows:
25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5,
20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1
Represent them as a frequency distribution table with class size 1°C.

Construct a frequency table with equal class intervals from the following data on the monthly
wages (in rupees) of 28 laborers working in a factory, taking one of the class intervals as
210-230 (230 not included):
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292,
254, 278, 210, 240, 280, 316, 306, 215, 256, 236.

The blood groups of 30 students of class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B,O
Represent this data in the form of a frequency distribution table. Find out which is the most Common and which is the rarest blood group among these students.

Three coins were tossed 30 times. Each time the number of head occurring was noted down
as follows:
0        1        2        2        1        2        3        1       3        0
1        3        1        1        2        2        0        1       2        1
3        0        0        1        1        2        3        2       2        0

Thirty children were asked about the number of hours they watched T.V. programmers in the previous week. The results were found as follows:

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 – 10.
(ii)How many children watched television for 15 or more hours a week?

The daily minimum temperatures in degrees Ce1siu& recorded in a certain Arctic region are
as follows:
−12.5, −10.8, −18.6, −8.4, −10.8, −4.2, −4.8, −6.7, −13.2, −11.8, −2.3, 1.2, 2.6, 0, 2.4,
0, 3.2, 2.7, 3.4, 0, − 2.4, − 2.4, 0, 3.2, 2.7, 3.4, 0, − 2.4, − 5.8, -8.9, 14.6, 12.3, 11.5, 7.8,2.9.
Represent them as frequency distribution table taking − 19.9 to − 15 as the first class
interval.

Define cumulative frequency distribution.

Explain the difference between a frequency distribution and a cumulative frequency distribution.

The marks scored by 55 students in a test are given below:

Prepare a cumulative frequency table:

Following are the ages of360 patients getting medical treatment in a hospital on a day:

Construct a cumulative frequency distribution.

The water bills (in rupees) of 32 houses in a certain street for the period 1.1.98 to. 31.3.98 are given below:
56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59.
Tabulate the data and resent the data as a cumulative frequency table using 70-79 as one of the class intervals.

The number of books in different shelves of a library are as follows:
30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20
19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34,
38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25
28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23,
43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21.
Prepare a cumulative frequency distribution table using 45-49 as the last class interval.

Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.

The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:

(i) Represent this as a frequency distribution table.
(ii) Prepare a cumulative frequency table.

Given below is a cumulative frequency distribution table showing the ages of people living in a locality:

Prepare a frequency distribution table

Mark the correct alternative in each of the following: Tally marks are used to find

The difference between the highest and lowest values of the observations is called

The difference between the upper and the lower class limits is called

In the class intervals 10-20, 20-30, 20 is taken in

In a frequency distribution, the mid-value of a class is 15 and the class intervals is 4. The lower limit of the class is

The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are:

The number of times a particular item occurs in a given data is called its

The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is

The following marks were obtained by the students in a test:
81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62
The range of the marks is

Tallys are usually marked in a bunch of

Let l be the lower class limit of a class-interval in a frequency distribution and m be the mid point of the class. Then, the upper class limit of the class is