Find the median of the following frequency distribution table: Variable x 4 6 8 10 12 14 16 Frequency f 2 4 5 3 2 1 4

Given table Variable x Frequency f Cumulative Frequency 4 2 2 6 4 6 8 5 11 10 3 14 12 2 16 14 1 17 16 4 21 ∑ f = 21 Here, N = ∑ f = 21 (odd number) Median = value of the N + 1 2 th term = 21 + 1 2 th term = 11 th term = 8 (From table) Hence, median is 8 .

Let log a m n = x ⇒ m n = a x ⇒ a x = m n . . . . . i Let log a m = b , log a n = c ⇒ m = a b , n = a c m n = a b a c = a b - c From equation i , ⇒ a x = a b - c ⇒ x = b - c ⇒ log a m n = log a m - log a n Hence, log m n = log m - log n .

Write the formula of Compound amount.

Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal. The compound interest is calculated, after calculating the total amount over a period of time, based on the rate of interest, and the initial principal. For an initial principal of P , rate of interest per annum of r , time period t in years, the formula for calculation of amount is as follows. Compound Amount A = P × 1 + r 100 t Compound interest = Compound amount - Principal amount = P × 1 + r 100 t - P

Find the median of the following frequency distribution table: Variable x 4 6 8 10 12 14 16 Frequency f 2 4 5 3 2 1 4

Given table Variable x Frequency f Cumulative Frequency 4 2 2 6 4 6 8 5 11 10 3 14 12 2 16 14 1 17 16 4 21 ∑ f = 21 Here, N = ∑ f = 21 (odd number) Median = value of the N + 1 2 th term = 21 + 1 2 th term = 11 th term = 8 (From table) Hence, median is 8 .

The following table shows the ages of the patients admitted in a hospital during a year : Age (in years) 5 - 15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 Number of patients 6 11 21 23 14 5 Find the mode of the data given above.

We have, Age (in years) 5 - 15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 Number of patients 6 11 21 23 14 5 We observe that the class 35 - 45 has the maximum frequency. So, it is the modal class such that l = 35 , h = 10 , f = 23 , f 1 = 21 , f 2 = 14 Therefore, Mode = l + f - f 1 2 f - f 1 - f 2 × h = 35 + 23 - 21 2 23 - 21 - 14 × 10 = 35 + 20 11 = 35 + 1 . 82 = 36 . 82 Hence, the mode of the data is 36 . 82

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>Madhya Pradesh Board-2018>Q 5

EASY

10th Madhya Pradesh Board

IMPORTANT

Earn 100

Find the arithmetic mean of $47, 53, 49, 60, 39, 42, 53, 52, 50, 55$ .

Important Questions on Statistics

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>Madhya Pradesh Board-2018>Q 6

Find the median of the following frequency distribution table:

Variable $x$	$4$	$6$	$8$	$10$	$12$	$14$	$16$
Frequency $f$	$2$	$4$	$5$	$3$	$2$	$1$	$4$

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>Madhya Pradesh Board-2018>Q 7

Write two merits and one demerit of median.

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>Madhya Pradesh Board-2019>Q 8

What will be the Arithmetic mean of

1, 2, 3, 4, 5 ?

EASY

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>Madhya Pradesh Board-2019>Q 9

Write the formula of the median.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>Madhya Pradesh Board-2019>Q 10

A survey conduct on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family member in a household

$\begin{array}{lccccc} Family size & 1 - 3 & 3 - 5 & 5 - 7 & 7 - 9 & 9 - 11 \\ Number of families & 7 & 8 & 2 & 2 & 1 \end{array}$

Find the Mode of this data.

MEDIUM

10th Madhya Pradesh Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>Madhya Pradesh Board-2019>Q 11

In given data

$\begin{array}{l} Class Interval & Number of students \\ 10 - 25 & 2 \\ 25 - 40 & 3 \\ 40 - 55 & 7 \\ 55 - 70 & 6 \\ 70 - 85 & 6 \\ 85 - 100 & 6 \end{array}$