Question

The arithmetic mean of 10 values is 35.5. If nine values are 20, 23, 37, 48, 29,
33, 45, 40, 45, find the tenth value.
the​

Answer 1

Answer:

35

Step-by-step explanation:

Let the tenth number be x

So the mean of all the ten numbers will be:

sum of all numbers / 10

So, (20+23+37+48+29+33+45+40+45+x)/10

(320+x)/10 = 35.5

320+x = 355

x = 355 - 320

x = 35

Answer 2

$\bf{Solution:-}$

Given :-

• Arthemetic of 10 values is 35.5
• The nine values in data are 20,23,37,48,29,33,45,45

To find :-

• 10th Observation

Formula to know:-

$\bf{Mean} = \bf\dfrac{Sum\:of\:observations}{No\:of\:observations}$

Solution:-

Let the tenth value of observation is x

Sum of observations =

(Including 10th observation)

= 20+ 23+ 37+ 48+ 29 +33+ 45+ 40+ 45+ x

= 320 + x

Sum of observations = 320+x

No.of observations = 10

$\bf{Mean} = \bf\dfrac{Sum\:of\:observations}{No\:of\:observations}$

Plugging values:-

$\bf{35.5}$= $\bf\dfrac{320+x}{10}$

$\bf\dfrac{355}{10}$ = $\bf\dfrac{320+x}{10}$

320+ x = 355

x = 355- 320

x = 35

So, the 10th value in data is 35

____________________________

Verification:-

If we Substitute the value of x That means The mean should be equal to 35.5

Already we know

Sum of observations = 320+x

x = 35

Sum of observations = 320+35

Sum of observations = 355

No.of observations = 10

$\bf{Mean} = \bf\dfrac{Sum\:of\:observations}{No\:of\:observations}$

Mean = 355/10

Mean = 35.5

Hence It equal to 35.5

Verified !