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

The following table gives the ages of $130$ members of a club.

Age (in years)	20 and under 25	25 and under 30	30 and under 35	35 and under 40	40 and under 45
No. of members	2	?	29	43	?

If the median age is $37.33$ years, find the missing frequencies.

Accepted Answer

We construct the following table as under:

Age (in years) 20-25 25-30 30-35 35-40 40-45

No. of member $f_{i}$ 2 $f_{1}$ 29 43 $f_{2}$

Cumulative frequency 2 $2 + f_{1}$ $31 + f_{1}$ $74 + f_{1}$ $74 + f_{1} + f_{2}$

Since total frequency $n = \underset{}{\sum f_{i} = 130} \Rightarrow 74 + f_{1} + f_{2} = 130 \Rightarrow f_{1} + f_{2} = 56 . . . . . (1)$

$∴ \frac{n}{2} i . e . 65^{th}$ observation lies in the class $35 - 40$ .

Thus, $35 - 40$ be the median class.

Thus $l = 35; f = 43; c = 31 + f_{1}; i = 5$

We know that,

$Median = l + \frac{\frac{n}{2} - c}{f} \times i$

$= 35 + \frac{65 - 31 - f_{1}}{43} \times 5$

Also given median age $= 37.33$ years

$37.33 = 35 + \frac{34 - f_{1}}{43} \times 5 \Rightarrow 2.33 = \frac{(34 - f_{1}) 5}{43}$

$\Rightarrow 100.19 = 170 - 5 f_{1} \Rightarrow 5 f_{1} = 69.81 \Rightarrow f_{1} = 13.96$

$∴ f_{1} = 14$

$∴$ From $(1)$ ; $f_{2} = 56 - 14 = 42$

Hence, the value of $f_{1} and f_{2}$ are $14 and 42$

Variate	$15$	$18$	$20$	$22$	$25$	$27$	$30$
Frequency	$4$	$6$	$8$	$9$	$7$	$8$	$6$

Variate	$25$	$31$	$34$	$40$	$45$	$48$	$50$	$60$
Frequency	$3$	$8$	$10$	$15$	$10$	$9$	$9$	$2$

The following table gives the ages of $130$ members of a club.

Age (in years) 20 and under 25 25 and under 30 30 and under 35 35 and under 40 40 and under 45

No. of members 2 ? 29 43 ?

If the median age is $37.33$ years, find the missing frequencies.

Important Questions on Statistics

Learn and Prepare for any exam you want !

The following table gives the ages of 130 members of a club. Age (in years) 20 and under 25 25 and under 30 30 and under 35 35 and under 40 40 and under 45 No. of members 2 ? 29 43 ? If the median age is 37.33 years, find the missing frequencies.

Important Questions on Statistics

Learn and Prepare for any exam you want !

The following table gives the ages of $130$ members of a club.

Age (in years) 20 and under 25 25 and under 30 30 and under 35 35 and under 40 40 and under 45

No. of members 2 ? 29 43 ?

If the median age is $37.33$ years, find the missing frequencies.