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Class 9 Maths Chapter 13 Question Answers - Statistics

Q1: For a particular year, following is the distribution of ages (in years) of primary school teachers in a district :

Class 9 Maths Chapter 13 Question Answers - Statistics

(i) Write the lower limit of first class interval.
(ii) Determine the class limits of the fourth class interval.
(iii) Find the class mark of the class 45 – 50.
(iv) Determine the class size.
Ans:

(i) First class interval is 15 – 20 and its lower limit is 15.
(ii) Fourth class interval is 30 – 35
Lower limit is 30 and upper limit is 35.
(iii) Class mark of the class 45 – 50 = 45 + 50 / 2 = 95/2 = 47.5
(iv) Class size = Upper limit of each class interval – Lower limit of each class interval
∴ Here, class size = 20 – 15 = 5

Q2: Find the mean of the following distribution :

Class 9 Maths Chapter 13 Question Answers - StatisticsAns:
Class 9 Maths Chapter 13 Question Answers - StatisticsNow,
Class 9 Maths Chapter 13 Question Answers - Statistics
= 19

Q3: In figure, there is a histogram depicting daily wages of workers in a factory. Construct the frequency distribution table.
Class 9 Maths Chapter 13 Question Answers - StatisticsAns:

Class 9 Maths Chapter 13 Question Answers - Statistics
Q4: Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in ascending order. The median of the data is 24. Find the value of x.
Ans:

Here, the arranged data is 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43
Total number of observations = 10
Class 9 Maths Chapter 13 Question Answers - Statistics
But median of data is 24 (given)
⇒ 3x−12 / 2 = 24
⇒ 3x – 12 = 48
⇒ 3x = 60
⇒ x = 20
∴ The value of x = 20

Q5: Draw a histogram for the given data :
Class 9 Maths Chapter 13 Question Answers - StatisticsAns:

Let us represent class-intervals along x-axis and corresponding frequencies along y-axis on
a suitable scale, the required histogram is as under : 
Class 9 Maths Chapter 13 Question Answers - Statistics

Q6: Given are the scores (out of 25) of 9 students in a Monday test :
14, 25, 17, 22, 20, 19, 10, 8 and 23
Find the mean score and median score of the data.
Ans:

Ascending order of scores is :
8, 10, 14, 17, 19, 20, 22, 23, 25
Now, Mean Score = Class 9 Maths Chapter 13 Question Answers - Statistics
Class 9 Maths Chapter 13 Question Answers - Statistics
= Class 9 Maths Chapter 13 Question Answers - Statistics
= 19 marks

Q7: Draw a histogram of the weekly pocket expenses of 125 students of a school given below :
Class 9 Maths Chapter 13 Question Answers - StatisticsAns: 
Here, the class sizes are different, so calculate the adjusted frequency for each class by using the formula.
Minimum class size Frequency density or adjusted frequency for a class
= Class 9 Maths Chapter 13 Question Answers - Statistics
Here, the minimum class size = 10 – 0 = 10
Class 9 Maths Chapter 13 Question Answers - StatisticsLet us represent weekly pocket money along x-axis and corresponding adjusted frequencies along y-axis on a suitable scale, the required histogram is as given below :
Class 9 Maths Chapter 13 Question Answers - Statistics
Q8: The weight in grams of 35 mangoes picked at random from a consignment are as follows:
131, 113, 82, 75, 204, 81, 84, 118, 104, 110, 80, 107, 111, 141, 136, 123, 90, 78, 90, 115, 110, 98, 106, 99, 107, 84, 76, 186, 82, 100, 109, 128, 115, 107, 115 From the grouped frequency table by dividing the variable range into interval of equal width of 20 grams, such that the mid-value of the first class interval is 70 g. Also, draw a histogram.
Ans:

It is given that the size of each class interval = 20 and the mid-value of the first class interval is 70.
Let the lower limit of the first class interval be a, then its upper limit = a + 20
Class 9 Maths Chapter 13 Question Answers - Statistics
⇒ a = 70 – 10 = 60
Thus, the first class interval is 60 – 80 and the other class-intervals are 80 – 100, 100 – 120, 120 – 140, 140 – 160, 160 – 180, 180 – 200 and 200 – 220.
So, the grouped frequency table is as under :
Class 9 Maths Chapter 13 Question Answers - StatisticsClass 9 Maths Chapter 13 Question Answers - StatisticsLet us represent weight (in g) along x-axis and corresponding frequencies along y-axis on a suitable scale, the required histogram is as under :
Class 9 Maths Chapter 13 Question Answers - Statistics
Q9: Find the mean salary of 60 workers of a factory from the following table :
Class 9 Maths Chapter 13 Question Answers - StatisticsAns:

Class 9 Maths Chapter 13 Question Answers - StatisticsClass 9 Maths Chapter 13 Question Answers - Statistics
Hence, mean salary of 60 workers is ₹5083.33.

Q10: In a school marks obtained by 80 students are given in the table. Draw a histogram. Also, make frequency polygon.

Class 9 Maths Chapter 13 Question Answers - StatisticsAns:
∴ Lower limit of first class interval is 305 – 10/2 = 300
Upper limit of first class interval is 305 + 10/2 = 310
Thus, first class interval is 300 – 310
Class 9 Maths Chapter 13 Question Answers - StatisticsRequired histogram and frequency polygon is given on the graph paper.
Class 9 Maths Chapter 13 Question Answers - Statistics

Q11: The following two tables gives the distribution of students of two sections according to the marks obtained by them :Class 9 Maths Chapter 13 Question Answers - StatisticsRepresent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Ans:

The class marks are as under :
Class 9 Maths Chapter 13 Question Answers - StatisticsLet us take class marks on X-axis and frequencies on Y-axis. To plot frequency polygon of Section-A, we plot the points (5, 3), (15, 9), (25,17), (35,12), (45, 9) and join these points by (15,19). line segments. To plot frequency polygon of Section-B, we plot the points (5, 5), (15, 19), (25, 15), (35, 10), (45, 1) on the same scale and join these points by dotted line segments.
Class 9 Maths Chapter 13 Question Answers - StatisticsFrom the above two polygons, clearly the performance of Section A is better.

The document Class 9 Maths Chapter 13 Question Answers - Statistics is a part of the Class 9 Course Mathematics (Maths) Class 9.
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