Question

Find the unknown values in the following table,
Class interval
0-10
10 - 20
20-30
30 - 40
40 - 50
frequency
5
7
x2
5
x4
Cumulative frequency
5
x1
18
X3
30
​

Answer 1

Answer:

Step-by-step explanation:

5+7=x1=12

12+x2=18=>x2=6

18+5=x3=23

23+x4=30=>x4=7

Answer 2

Answer:

The unknown values in the given table are:

• $x_{1}$ = $12$,
• $x_{2}$ = $6$,
• $x_{3}$ = $23$, and
• $x_{4}$ = $7$.

Step-by-step explanation:

Given data,

Class interval         Frequency             Cumulative frequency

$0-10$                             $5$                                      $5$

$10-20$                            $7$                                      $x_{1}$

$20-30$                            $x_{2}$                                    $18$

$30-40$                            $5$                                      $x_{3}$

$40-50$                            $x_{4}$                                    $30$

To find: The unknown values in the given table =?

As we know,

• Cumulative frequency is the sum of the frequency of the particular class and the prior classes.

Therefore, we can write the cumulative frequencies as:

Class interval         Frequency             Cumulative frequency

$0-10$                             $5$                                      $5$ ( $5 +0$ )

$10-20$                            $7$                                      $x_{1}$ ( $7+5$ )

$20-30$                            $x_{2}$                                    $18$ ( $x_{2} +7 +5$ )

$30-40$                            $5$                                      $x_{3}$ ( $5 +x_{2} +7 +5$ )

$40-50$                            $x_{4}$                                    $30$ ( $x_{4} +5 +x_{2} + 7 +5$ )

From the table, we can see that:

• $x_{1}$ = $7+5$ = $12$

And,

• $x_{2} + 7 +5= 18$
• $x_{2} + 12= 18$

Therefore,

• $x_{2}$ = $6$

Also,

• $x_{3} = 5 +x_{2} +7 +5$
• $x_{3} = 17 +x_{2}$

As calculated above, $x_{2}$ = $6$;

• $x_{3} = 17+ 6$
• $x_{3} = 23$

And,

• $x_{4} +5 +x_{2} + 7 +5 = 30$

As calculated above, $x_{2}$ = $6$;

• $x_{4} +5 +6 + 7 +5 = 30$
• $x_{4} +23 = 30$
• $x_{4}= 7$

Hence, the value of $x_{1}$ is $12$, $x_{2}$ is $6$, $x_{3}$ is $23$ and $x_{4}$ is $7$.