Question

Class interval 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 5 3 4 3 4 7 9 7
Find mean median and mode

Answer 1

Mean = 5.25, Median = 4.5, Mode = 3, 4 and 7

Step-by-step explanation:

Given Data

There are eight intervals with eight frequencies

The frequencies are 5, 3, 4, 3, 4, 7, 9 and 7

To find mean, median, mode

Mean - mean is like normal average, which is the sum of all the given data and divide them by the number of data

Median is the middle number from the given data after arranged in ascending order.

Mode is defined as the number which is repeated more number of times than any other number in the given data

$Mean =\frac{ 5 + 3 + 4 + 3 + 4 + 7 + 9 + 7 }{8}$  

$Mean = \frac{42}{8}$

Mean = 5.25

Median : We have to arrange the given data in ascending order

3, 3, 4, 4, 5, 7, 7, 9

There are eight terms in the given data. So add the 4th and 5th term and divide them by 2.

$Median = \frac{ 4 + 5 }{2}$

Median = 4.5

Mode : In the given data, there are three repeated numbers and they are 3, 4 and 7.

Mode = 3, 4 and 7

For the given frequencies 5, 3, 4, 3, 4, 7, 9, 7 mean is 5.25, median is 4.5 and mode is 3, 4 and 7

To Learn More ...

1. https://brainly.in/question/2484750

2. https://brainly.in/question/7329181

Answer 2

Therefore Mean=44.29

                 Median =54.29

                 Mode =65    

Step-by-step explanation:

Class interval      frequency(f)    Mid-class(x)       f.x       cf

0-10                           5                      5                 25        5

10-20                         3                     15                 45        8

20-30                        4                     25                100      12

30-40                        3                     35                105       15

40-50                       4                      45               90         19

50-60                      7                       55               385       26   (median class)

60-70                       9                      65               585       35(mode class)

70-80                      7                       75               525        42

                           _____                                     ______

                       n=Σf=42                                Σfx=1860

$Mean = \frac{\sum f.x}{\sum f}$

          $=\frac{1860}{42}$

          =44.29

Median:

Median class $=(\frac{\sum f}{2})^{th}$ observation

                     $=(\frac{42}{2}){th}$ observation

                    $=21^{th}$ observation

$21^{th}$ observation lies in the class 50-60

Class interval of median = 50-60

Now L= lower limit of median class = 50

n= total frequency = 42

cf = cumulative frequency of the preceding class of the median class=19

f= frequency of the median class= 7

c = length of median class=(60-50)=10

$M=L+\frac{\frac{n}{2} -cf}{f} .c$

     $=50+\frac{\frac{42}{2}-19 }{7} .10$

    $=50+\frac{21-19 }{7} .10$

   $=50+\frac{3\times 10}{7}$

   =54.29

Mode:

The maximum frequency is 9.The maximum frequency is contained by the class 60-70.

Hence the mode class is 60-70.

L = lower limit of mode class= 60

f₁= frequency of mode class =9    

f₀= frequency of preceding class of mode class=7

f₂= frequency of the succeeding class of the mode class=7

c=class length of mode class =(70-60)=10

$Z=L+\frac{f_1-f_0}{2f_1-f_0-f_2} .c$

    $=60+\frac{9-7}{(2\times9)-7-7} \times 10$

   =65

Therefore Mean=44.29

                 Median =54.29

                 Mode =65