AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:
Number of letters 1-4 4-7 7-10 10-13 13-16 16-19
Number of surnames 6 30 40 16 4 4
Determine the number of median letters in the surnames. Find the number of mean letters in the surnames and also, find the size of modal in the surnames.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 1.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

To calculate median:

Class Interval	Frequency	Cumulative Frequency
1-4	6	6
4-7	30	36
7-10	40	76
10-13	16	92
13-16	4	96
16-19	4	100

Given:

n = 100 & $\frac{n}{2}$ = 50

Median class = 7-10

Therefore, l = 7, C_f = 36, f = 40 & h = 3

Ncert solutions class 10 chapter 14-6

Median = 7+( $\frac{50 - 36}{40}$ ) × 3

Median = 7+ $\frac{42}{40}$

Median=8.05

Calculate the Mode:

Modal class = 7-10,

Where, l = 7, f₁ = 40, f₀ = 30, f₂ = 16 & h = 3

Ncert solutions class 10 chapter 14-7

Mode = 7+( $\frac{40 - 30}{80 - 30 - 16}$ ) × 3

= 7+ $\frac{30}{34}$

= 7.88

Therefore mode = 7.88

Calculate the Mean:

Class Interval	f_i	x_i	f_ix_i
1-4	6	2.5	15
4-7	30	5.5	165
7-10	40	8.5	340
10-13	16	11.5	184
13-16	4	14.5	51
16-19	4	17.5	70
	Sum f_i = 100		Sum f_ix_i = 825

Mean = x̄ = $\frac{\sum_{} f_{i} x_{i}}{\sum_{} f_{i}}$

Mean = $\frac{825}{100}$ = 8.25

Therefore, mean = 8.25

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!