Download App

Stastics — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsStastics5 Marks
Question
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the 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 median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
✓

Answer

First, we will convert the graph given into tabular form as shown below:
Class interval Frequency ($f_i$) Mid value ($x_i​​​​​​​$) $f_ix_i$ Cumulative Frequency
1 – 4 6 2.5 15 6
4 – 7 30 5.5 165 36
7 – 10 40 8.5 340 76
10 – 13 16 11.5 184 92
13 – 16 4 14.5 58 96
16 – 19 4 17.5 70 100
  N = $\sum$$f_i$ = 100   $\Sigma f_i x_i$ = 832  
  1. N = 100
    Mean = $\frac { \Sigma f_i x_i } { N } = \frac { 832 } { 100 }$ = 8.32
  2. $ \frac{N}{2} = \frac{{100}}{2}$ = 50
    The cumulative frequency just greater than $\frac {N} {2}$ is 76, then the median class is 7 - 10 such that
    l = 7, h = 10 - 7 = 3, f = 40, F = 36
    Median = l + $\frac { \frac { N } { 2 } - F } { f } \times$ h
    = 7 + $\frac { 50 - 36 } { 40 } \times$ 3
    $= 7 + \frac {42} {40}$ = 7 + 1.05 = 8.05
  3. Mode = 3 Median - 2 Mean
    = 3 $\times$ 8.05 - 2 $\times$ 8.32 = 7.51

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Stastics→Stastics — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Find a relation between x and y, if the points A(2, 1), B(x, y), and C(7, 5) are collinear.
→
A circular park is surrounded by a rod 21m wide. If the radius of the park is 105m, find the area of the road.
→
From the top of a hill, the angles of depression of two consecutive kilometre stones due east are fouud to be 45° and 30° respectively.
Find the height of the hill.
→
Find the maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils.
→
Show graphically that the following system of equation is in-consistent (i.e. has no solution):
3x - 5y = 20
6x - 10y = -40
→
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Weight(in kg) Number of students
40-45 2
45-50 3
50-55 8
55-60 6
60-65 6
65-70 3
70-75 2
→
If the points $(-2, -1), (1, 0), (x, 3)$ and $(1, y)$ form a parallelogram, find the values of x and y.
→
Find the roots of the following equations, if they exist, by applying the quadratic formula:$\frac{\text{m}}{\text{n}}\text{x}^2+\frac{\text{n}}{\text{m}}=1-2\text{x}$
→
A man is employed to count Rs. 10710. He counts at the rate of Rs. 180 per minute for half an hour. After this he counts at the rate of Rs. 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
→
A wire is bent to form a square enclosing an area of $484m^2$​​​​​​​. Using the same wire, a circle is formed. Find the area of the circle.
→