Name: Variance and Standard Deviation for Ungrouped Distribution
Uploaded: 2019-07-19
Duration: 6 min 21 s
Description: In this video, let us learn to find the variance and standard deviation of ungrouped data. We will also learn the formula to find the discrete frequency dist...

Question

Calculate the median and mode for the frequency distribution given below:

Variable	$10 - 13$	$13 - 16$	$16 - 19$	$19 - 22$	$22 - 25$	$25 - 28$	$28 - 31$	$31 - 34$	$34 - 37$	$37 - 40$
Frequency	$8$	$15$	$27$	$51$	$75$	$54$	$36$	$18$	$9$	$7$

Accepted Answer

Variable Frequency $10 - 13$ Cumulative Frequency

$10 - 13$ $8$ $19 - 22$

$13 - 16$ $15$ $23$

$16 - 19$ $27$ $50$

$19 - 22$ $51$ $101$

$15$ $75$ $176$

$25 - 28$ $54$ $230$

$28 - 31$ $36$ $266$

$31 - 34$ $18$ $284$

$34 - 37$ $9$ $293$

$37 - 40$ $7$ $300$

Here, $N = Σ f = 300$

So, $\frac{N}{2} = \frac{300}{2} = 150$

We Notice That $150^{th}$ value lies in class $22 - 25$ ,

Therefore, $22 - 25$ is the median class.

We know,

Median $15$

$l =$ the lower limit of median class $= 22$ ,

Frequency of the median class $=$ $f = 75$ ,

Cumulative frequency of the class preceding the median class $= C = 101$ ,

Width of the median class $= h = 3$ ,

Sum of all frequencies $= N$ ,

Median $=$ $22 + \frac{(150 - 101)}{75} \times 3$

$= 22 + 1.96$

Median $= 23.96$

Here, the highest frequency is $75,$ corresponding to this modal class is $(22 - 25)$ .

Lower limit of the modal class $= l = 22$ ,

Frequency of the modal class $= f_{m} = 75$ ,

Frequency of the class preceding the modal class $= f_{m - 1} = 51$ ,

Frequency of the class succeeding the modal class $= f_{m + 1} = 54$ ,

$h = 3$ ,

Mode $= l + \frac{(f_{m} - f_{m - 1})}{(2 f_{m} - f_{m - 1} - f_{m + 1})} \times h$

$= 22 + (\frac{75 - 51}{2 \times 75 - 51 - 54}) \times 3$

$= 22 + \frac{24 \times 3}{45}$

Mode $= 23.6$

Hence, median $= 23.96$ ,

Mode $= 23.6$ .

Wages $(₹)$	Number of workers
Less than $10$	$3$
Less than $20$	$12$
Less than $30$	$27$
Less than $40$	$57$
Less than $50$	$75$
Less than $60$	$80$

Height (in $cm$ )	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$	$175 - 180$	$180 - 185$
Number of workers	$6$	$12$	$18$	$20$	$13$	$8$	$6$

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Number of Students	$12$	$20$	$30$	$38$	$24$	$16$	$12$	$8$

Height (in $cm$ )	$121 - 130$	$131 - 140$	$141 - 150$	$151 - 160$	$161 - 170$	$171 - 180$
Number of pupils	$12$	$16$	$30$	$20$	$14$	$8$

Class	$1 - 100$	$101 - 200$	$201 - 300$	$301 - 400$	$401 - 500$	$501 - 600$	$601 - 700$	$701 - 800$
Frequency	$23$	$25$	$35$	$60$	$45$	$39$	$25$	$16$

Calculate the median and mode for the frequency distribution given below:

Variable $10 - 13$ $13 - 16$ $16 - 19$ $19 - 22$ $22 - 25$ $25 - 28$ $28 - 31$ $31 - 34$ $34 - 37$ $37 - 40$

Frequency $8$ $15$ $27$ $51$ $75$ $54$ $36$ $18$ $9$ $7$

Important Questions on Statistics

Learn and Prepare for any exam you want !

$Weight (g)$	$110 - 119$	$120 - 129$	$130 - 139$	$140 - 149$	$150 - 159$	$160 - 169$	$170 - 179$	$180 - 189$
Frequency	$5$	$7$	$12$	$20$	$16$	$10$	$7$	$3$

Profit (in lakhs in $₹$ ) more than or equal to	$5$	$10$	$15$	$20$	$25$	$30$	$35$
Number of shops $(c . f)$	$30$	$28$	$16$	$14$	$10$	$7$	$3$

Calculate the median and mode for the frequency distribution given below: Variable 10-13 13-16 16-19 19-22 22-25 25-28 28-31 31-34 34-37 37-40 Frequency 8 15 27 51 75 54 36 18 9 7

Important Questions on Statistics

Learn and Prepare for any exam you want !

Calculate the median and mode for the frequency distribution given below:

Variable $10 - 13$ $13 - 16$ $16 - 19$ $19 - 22$ $22 - 25$ $25 - 28$ $28 - 31$ $31 - 34$ $34 - 37$ $37 - 40$

Frequency $8$ $15$ $27$ $51$ $75$ $54$ $36$ $18$ $9$ $7$