Question

OR
From the following distribution, find the median :
Classes : 500 - 600 600 – 700 700 - 800 800 - 900 900 - 1000
Frequency: 36 | 32 | 32 | 20
30​

Answer 1

Answer:

Median = 721.875

Step-by-step explanation:

We are given the following frequency distribution;

     Classes               Frequency (f)                 Cumulative frequency (cf)

   500 - 600                    36                                            36

    600 - 700                    32                                            68

    700 - 800                    32                                            100

    800 - 900                    20                                            120

    900 - 1000                  30                                             150

                                      ∑f = 150  

Firstly, we will calculate $\frac{N}{2}$, (where N = ∑f), $\frac{N}{2}$ = $\frac{150}{2}$ = 75.

So, the value of cumulative frequency just greater than or equal to 75 is 100.

Therefore, median class is 700 - 800 .

Now, Median formula =   $x_L + \frac{\frac{N}{2} -cf}{f_m}*c$

where, $x_L$ = lower limit of median class = 700

             N =  ∑f = 150    

             $f_m$ = frequency of median class = 32

             cf = cumulative frequency just above the median class = 68

              c = width of class interval = 100

So, Median = $700 + \frac{\frac{150}{2} -68}{32}*100$

                   = $700 + \frac{7}{32} *100$ = 700 + 21.875 = 721.875

Therefore, Median of given distribution is 721.875 .

Answer 2

Step-by-step explanation:

Median = 721.875

Step-by-step explanation:

We are given the following frequency distribution;

Classes Frequency (f) Cumulative frequency (cf)

500 - 600 36 36

600 - 700 32 68

700 - 800 32 100

800 - 900 20 120

900 - 1000 30 150

∑f = 150

Firstly, we will calculate \frac{N}{2}

2

N

, (where N = ∑f), \frac{N}{2}

2

N

= \frac{150}{2}

2

150

= 75.

So, the value of cumulative frequency just greater than or equal to 75 is 100.

Therefore, median class is 700 - 800 .

Now, Median formula = x_L + \frac{\frac{N}{2} -cf}{f_m}*cx

L

+

f

m

2

N

−cf

∗c

where, x_Lx

L

= lower limit of median class = 700

N = ∑f = 150

f_mf

m

= frequency of median class = 32

cf = cumulative frequency just above the median class = 68

c = width of class interval = 100

So, Median = 700 + \frac{\frac{150}{2} -68}{32}*100700+

32

2

150

−68

∗100

= 700 + \frac{7}{32} *100700+

32

7

∗100 = 700 + 21.875 = 721.875