Question

A class teacher has the following attendance record of 40 students of a class for the whole term find the mean number of days a student was present out of 56 days in the term number of days 35-38 38-41 41-44 44-47 47-50 50-53 52-56 number of students 1 3 4 4 7 10 11

Answer 1

Hey Dear,

● Answer -

Mean = 49 days

◆ Explanation -

For this we have to calculate fi.xi for each class.

For class 35-38,

fixi = 36.5 × 1

fixi = 36.5

For class 38-41,

fixi = 39.5 × 3

fixi = 118.5

For class 41-44,

fixi = 42.5 × 4

fixi = 170

For class 44-47,

fixi = 45.5 × 4

fixi = 182

For class 47-50,

fixi = 48.5 × 7

fixi = 339.5

For class 50-53,

fixi = 51.5 × 10

fixi = 515

For class 53-56,

fixi = 54.5 × 11

fixi = 599.5

Summation fixi will be -

Σfixi = 36.5 + 118.5 + 170 + 182 + 339.5 + 515 + 599.5

Σfixi = 1961

Mean no of days each student attended school will be -

Mean = Σfixi / Σfi

Mean = 1961 / 40

Mean = 49.05 days

Therefore, mean no of days a student was present in school is 49 days.

Best luck...

Answer 2

Given : A class teacher has the following attendance record of 40 students of a class for the whole team.

Complete Data is:

35-38 38-41 41-44 44-47 47-50 50-53 53-56

1             3          4        4        7          10        11

To Find : the mean number of days a student was present out of 56 days  

Solution:

A = Assume mean = 48.5    , h = 3

Days        f        Mean     u =(Mean - A)/3    fu

35-38      1          36.5      -4                       -4

38-41       3         39.5      -3                      -9

41-44       4         42.5      -2                       -8

44-47       4        45.5      -1                        -4

47-50       7        48.5        0                      0

50-53      10       51.5        1                       10

53-56      11        54.5        2                     22

  Total    40                                                 7

$\text{Mean}=\overline{x}=A+h \times \frac{\sum fu}{\sum f}$

48.5  +  3 * 7 / 40

= 48.5 + 0.525

= 49.025

mean number of days a student was present out of 56 days = 49.025

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