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Home » 4. The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures
4. The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures
CBSE | Class 10 | Exercise 14.2 | Maths | NCERT | Statistics
4. The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures
No of Students per teacherNumber of states / U.T
15-203
20-258
25-309
30-3510
35-403
40-450
45-500
50-552

Solution:

Given information:

Modular class = 30 – 35,

l = 30,

Class width (h) = 5,

fm = 10, f1 = 9 and f2 = 3

Mode Formula:

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> Mode\text{ }=\text{ }l+\text{ }\left[ \left( fm-f1 \right)/\left( 2fm-f1-f2 \right) \right]\times h \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

Substitute the qualities in the given recipe

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> Mode\text{ }=\text{ }30+\left( \left( 10-9 \right)/\left( 20-9-3 \right) \right)\times 5 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> Mode\text{ }=\text{ }30+\left( 5/8 \right)\text{ }=\text{ }30+0.625 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> Mode\text{ }=\text{ }30.625 \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

Accordingly, the method of the given information = 30.625

Computation of mean:

Discover the midpoint utilizing the recipe, xi =(upper limit +lower limit)/2

Class Interval      Frequency (fi)     Mid-point (xi)     fixi

15-20     3             17.5       52.5

20-25     8             22.5       180.0

25-30     9             27.5       247.5

30-35     10           32.5       325.0

35-40     3             37.5       112.5

40-45     0             42.5       0

45-50     0             47.5       0

50-55     2             52.5       105.5

Total fi = 35                       Sum fixi = 1022.5

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> Mean\text{ }=\text{ }x\text{ }=\text{ }\sum fixi/\sum fi \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

= 1022.5/35

= 29.2 In this manner, mean = 29.2

i

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