The weights of 60 boys are given in the following distribution tabW Weight(kg) 37 38 39 40 41 No. of boys 10 14 18 12 6 Find median

Weight (kg)x Number of boys Cumulative frequency 37 10 10 38 14 24 39 18 42 40 12 54 41 6 60 Number of terms = 60 Here n is even. So median = n 2 th term + n 2 + 1 th term 2 = 60 2 t h + 60 2 + 1 t h 2 madian = mean of 30 th and 31 st term = 39 + 39 2 = 78 2 = 39

The weights of 60 boys are given in the following distribution table: Weight(kg) 37 38 39 40 41 No. of boys 10 14 18 12 6 Find: Lower quartile

Weight (kg)x no. of boys cumulative frequency 37 10 10 38 14 24 39 18 42 40 12 54 41 6 60 x / o . of terms = 60 To find the lower quartile of a set of data, we can find the median of the data and then find the median of the first half. This strategy is similar to dividing a cake into halves, and then dividing one of the halves in half so that you end up with a quarter of the cake. Lower quartile ( Q , 1 ) = 60 4 term = 15 th term = 38

The weights of 60 boys are given in the following distribution table: Weight(kg) 37 38 39 40 41 No. of boys 10 14 18 12 6 Find: Upper quartile

Weight (kg)x no. of boys cumulative frequency 37 10 10 38 14 24 39 18 42 40 12 54 41 6 60 x / o . of terms = 60 The upper quartile is the median of the upper half of a data set. This is located by dividing the data set with the median and then dividing the upper half that remains with the median again, this median of the upper half being the upper quartile Upper quartile ( Q 3 ) 3 × 60 th 4 term = 45 th term = 40

The weights of 60 boys are given in the following distribution table: Weight(kg) 37 38 39 40 41 No. of boys 10 14 18 12 6 Find: Inter-quartile range

Weight (kg)x no. of boys cumulative frequency 37 10 10 38 14 24 39 18 42 40 12 54 41 6 60 x / o . of terms = 60 Interquartile range:-When a data set has outliers, variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles. The first quartile, denoted Q 1 , is the value in the data set that holds 25% of the values below it Q 3 - Q 1 = 40 - 38 = 2

Estimate the median for the given data by drawing ogive: Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 4 9 15 14 8

Class Frequency Cumulative frequency 0 - 10 4 4 10 - 20 9 13 20 - 30 15 28 30 - 40 14 42 40 - 50 8 50 Number of terms = 50 Madian = 25 + 26 th 2 term = 25 . 5 th term. mark 25 . 5 on y - axis , draw a line parallel to x - axis , meets the curse at A , from A draw a ⊥ to x - axis , Which meds x - axis at B . B is the median = 28 .

By drawing an ogive; estimate the median for the following frequency distribution: Weight (kg) 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 Number of boys 11 25 12 5 2

Weight(kg) No. of boys Cumulative frequency 10 - 15 11 11 15 - 20 25 36 20 - 25 12 48 25 - 30 5 53 30 - 35 2 55 Number of terms = 55 Median = 55 + 1 th 2 term = 28 th term The value of B = 18 . 4 kg = median

From the following cumulative frequency table draw ogive and then use it to find: Median Marks (less than) 10 20 30 40 50 60 70 80 90 100 Cumulative Frequency 5 24 37 40 42 48 70 77 79 80

Marks(us than) Cumulative frequency 10 5 20 24 30 37 40 40 50 42 60 48 70 70 80 77 90 79 100 80 Number of terms = 80 So median = n 2 th term + n 2 + 1 th term 2 Median = 80 2 th term + 80 2 + 1 th term 2 Madian = 40 th term

From the following cumulative frequency table draw ogive and then use it to find: Lower quartile Marks (less than) 10 20 30 40 50 60 70 80 90 100 Cumulative Frequency 5 24 37 40 42 48 70 77 79 80

Marks(us than) cumulative frequency 10 5 20 24 30 37 40 40 50 42 60 48 70 70 80 77 90 79 100 80 x . o . of terms = 80 median = 40 th term Value of B = 40 Lower quartile ( Q 1 ) = 20 th term = 18 A quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic.

R K Bansal Solutions for Exercise 1: EXERCISE

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Attempt the practice questions from Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. Concise Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 6

The weights of $= \frac{39 + 39}{2} = \frac{78}{2} = 39$ boys are given in the following distribution tabW

Weight(kg)	$37$	$38$	$39$	$40$	$41$
No. of boys	$10$	$14$	$18$	$12$	$6$

Find median

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 6

The weights of $60$ boys are given in the following distribution table:

Weight(kg)	$37$	$38$	$39$	$40$	$41$
No. of boys	$10$	$14$	$18$	$12$	$6$

Find:

Lower quartile

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 6

The weights of $60$ boys are given in the following distribution table:

Weight(kg)	$37$	$38$	$39$	$40$	$41$
No. of boys	$10$	$14$	$18$	$12$	$6$

Find:

Upper quartile

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 6

The weights of $60$ boys are given in the following distribution table:

Weight(kg)	$37$	$38$	$39$	$40$	$41$
No. of boys	$10$	$14$	$18$	$12$	$6$

Find:

Inter-quartile range

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 7

Estimate the median for the given data by drawing ogive:

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$4$	$9$	$15$	$14$	$8$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 8

By drawing an ogive; estimate the median for the following frequency distribution:

Weight (kg)	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Number of boys	$11$	$25$	$12$	$5$	$2$

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 9

From the following cumulative frequency table draw ogive and then use it to find:

Median

Marks (less than)	$10$	$20$	$30$	$40$	$50$	$60$	$70$	$80$	$90$	$100$
Cumulative Frequency	$5$	$24$	$37$	$40$	$42$	$48$	$70$	$77$	$79$	$80$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 9

From the following cumulative frequency table draw ogive and then use it to find:

Lower quartile

Marks (less than)	$10$	$20$	$30$	$40$	$50$	$60$	$70$	$80$	$90$	$100$
Cumulative Frequency	$5$	$24$	$37$	$40$	$42$	$48$	$70$	$77$	$79$	$80$

R K Bansal Solutions for Exercise 1: EXERCISE

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

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