The mark distribution of 40 students in an exam is shown below. Find the stand

Sail E0 Webinar

Question

The mark distribution of 40 students in an exam is shown below. Find the standard deviation of the distribution.
$\begin{matrix} Marks & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 No. of Students & 7 & 10 & 12 & 6 & 5 \end{matrix}$

Options:

A . 10.28

B . 12.49

C . 14.76

D . 15.83

Answer: Option B
:
B

$\begin{matrix} X & F & F X & D = X - ¯ X & D^{2} & F D^{2} 5 & 7 & 35 & - 18 & 324 & 2268 15 & 10 & 150 & - 8 & 64 & 640 25 & 12 & 300 & 2 & 4 & 48 35 & 6 & 210 & 12 & 144 & 864 45 & 5 & 225 & 22 & 484 & 2420 \sum F = 40 & \sum F X = 920 & \sum F D^{2} = 6240 \end{matrix}$
$M e a n, ¯ X = \frac{\sum F X}{\sum F} = \frac{920}{40} = 23$
$σ = \sqrt{\frac{\sum F D^{2}}{\sum F}} = \sqrt{\frac{6240}{40}} = \sqrt{156} = 12.49$

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The number of years of education acquired by a sample of 100 adults in a locality is as follows. Years of education0&....in a locality is as follows. Years of education0−44−88−1212−1616−2020−24No. of people1022322484

Question 2. The average ambient temperatures (in degrees celsius) for a region for 15 years from 2001-2015 is given below. 2....28.9, 30.5, 29.5 Calculate the coefficient of range for the temperatures.

Question 3. The coefficient of variation of data pertaining to the goals scored by two teams A and B in a football season are 0.35....season are 0.35 and 0.72 respectively. The true statement is

Question 4. Given below is the Lorenz curve representing the percentage revenues of car manufacturing companies worldwide.The top 20....20 percentage of the companies generate what percentage of revenue?

Question 5. For a data set, the coefficient of range is 0.5. The largest observation is 12. Find the smallest observation. ....

Question 6. Data A has a mean of 100 and standard deviation of 10. Data B has a mean of 1000 and standard deviation of 50. Which d....and standard deviation of 50. Which data shows more variability?

Question 7. The square root of ___ is called standard deviation ....

Question 8. The distribution of weights of 50 students in a class is as follows. Weight (kg)40−4545−5050ȡ....as follows. Weight (kg)40−4545−5050−5555−6060−6565−70No. of students371112107 Calculate the standard deviation using the step deviation method.

Question 9. Relative measures of dispersion have the same units as that of the observations in the data. State true or false. ....

Question 10. Find the coefficient of mean deviation about median for the following cumulative frequency distribution: xfrequencyCu....deviation about median for the following cumulative frequency distribution: xfrequencyCumulative frequency221134233925458135482156930684347843884240

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

GPOE / GPA Combined 1 Free Mock Test SAIL JO E-0 2024

ICA Combined 1 Free Revision Test SAIL JO E-0

RDIC Review Test SAIL JO E-0

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

RSP Combined 1 Free Revision Test SAIL JO E-0