Question

inter house cricket match was organized by a school. Distribution of runs made by the students is given below. Find the median runs scored. Runs scored 0-20 20-40 40-60 60-80 80-100 Number of students 4 6 5 3 4​

Answer 1

Answer:

Median of the given data = 44 runs

Step-by-step explanation:

Given data

Runs scored        0-20   20-40   40-60   60-80   80-100

no of students       4          6           5             3            4  

Here we need to find median for the runs scored

to calculate the median for any data we need to calculate cumulative frequency as shown below

the given data can be rewrite as

    runs scored         no of students         cumulative frequency

    (class interval)          (frequency)

      0- 20                             4                             4                = 4

      20 -40                           6                             4+ 6           =10

      40 -60                           5                             4+ 6+ 5      = 15

      60- 80                           3                             4+6+5+ 3   = 18

      80 -100                          4                             4+6+5+3+4 = 22

                                                                              total (N) = 22      

⇒ n/2 = 22/2 = 11, then the median will lies in (40-60)  

⇒ the median class for given data is 40-60

⇒ the formula for median is given by = L + $[\frac{\frac{n}{2} + C.F }{f} ] h$  

here

 l = lower limit of the median class = 40

 n = number of observations = 22

C.F = cumulative frequency of class before  the median =10

 f = frequency of the median class = 5  

h = size of the class = 20

⇒ median =  40 + $[\frac{11 - 10}{5} ] 20$  

                 =  40 + $\frac{1}{5}$ × 20

                  = 40 + 4 = 44

⇒ median of the given data = 44 runs

Answer 2

Given : Data about Runs scored and number of players

To find : Median Runs Scored

Step-by-step explanation:

Solution:

Runs scored Frequency Cumulative Frequency

0-20              4                                       4

20-40              6                                       10

40-80              5                                       15

80-100              3                                       18

100-120              4                                       22

• Total frequency (n) = 22
• n/2 = 11; So 40-60 is the median class.
• l = 40, h = 20, cf = 10, f = 5
• Median = l+(n/2-cf/f)×h
• = 40 + (11-10/5) × 20
• = 44 runs
• Median Runs Scored are 44 .