Question

For a continuous data distribution, 10-20 with frequency 3, 20-30 with frequency 5, 30-40 with frequency 7and 40-50 with frequency 1, the value of Q_3 is

Answer 1

SOLUTION

GIVEN

For a continuous data distribution, 10-20 with frequency 3, 20-30 with frequency 5, 30-40 with frequency 7and 40-50 with frequency 1

TO DETERMINE

$\sf{The \: value \: of \: \: Q_3}$

EVALUATION

Here it is given that For a continuous data distribution, 10-20 with frequency 3, 20-30 with frequency 5, 30-40 with frequency 7and 40-50 with frequency 1

We draw the frequency table as below

$\begin{gathered} \begin{array}{|c|c| c| } \sf{Class \: Interval} & \sf{Frequency}& \sf{Cumulative \: freq.} \\ 10 - 20 & 3 & 3 \\20 - 30 & 5 & 8 \\30 - 40 & 7 & 15 \\40 - 50 & 1 & 16 \end{array}\end{gathered}$

Now N = 16

Therefore

$\displaystyle\sf{ \frac{3N}{4} = 12}$

Now cumulative frequency just greater than 12 is 15

So upper quartile class is 30 - 40

Thus we get

l = 30 , f = 7 , h = 10 , F = 8

$\displaystyle\sf{Q_3 = l + \frac{ \frac{3N}{4} - F }{f} \times h}$

$\displaystyle\sf{ \implies \: Q_3 = 30+ \frac{ 12 - 8 }{7} \times 10}$

$\displaystyle\sf{ \implies \: Q_3 = 30+ \frac{ 40 }{7} }$

$\displaystyle\sf{ \implies \: Q_3 = 30+ 5.7 }$

$\displaystyle\sf{ \implies \: Q_3 = 35.7 }$

FINAL ANSWER

$\boxed{ \: \: \displaystyle\sf{ \: Q_3 = 35.7 } \: \: }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. in 2,5,7,6,7,7,2, the mode is 7

https://brainly.in/question/38648591

2. Generally, what is the range of coefficient of skewness for data where the mode is ill-defined?(A) 0 to 1 (B) -1 to +1

https://brainly.in/question/26142979

3. if arithmetic mean of a seties is 45 and median is 40 then calculate the value of mode of that series

https://brainly.in/question/31548199