Question

the mean value of 160 data points is 500. a new series is created by increasing all the data points by 5 units. calculate the mean of the new series.

PLEASE I AM IN A REALLY BIG HURRY CAN SOMEONE ANSWER THIS WITH EXPLANATION

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Answer 1

Answer:

The mean (or average) of observations, as we know, is the sum of the values of all the

observations divided by the total number of observations. From Class IX, recall that if

x1

, x2,. . ., xn

are observations with respective frequencies f

1, f2

, . . ., fn

, then this

means observation x1

occurs f

1

times, x2 occurs f

2

times, and so on.

Now, the sum of the values of all the observations = f1x1 + f2x2 + . . . + fnxn, and

the number of observations = f1

+ f2

+ . . . + f

n

.

So, the mean x of the data is given by

x = 11 2 2

1 2

n n

n

fx fx fx

ff f

 

 

L

L

Recall that we can write this in short form by using the Greek letter Σ (capital

sigma) which means summation. That is,

STATISTICS

STATISTICS 261

x = 1

1

n

i i

i

n

i

i

f x

f









which, more briefly, is written as x =





i i

i

f x

f , if it is understood that i varies from

1 to n.

Let us apply this formula to find the mean in the following example.

Example 1 : The marks obtained by 30 students of Class X of a certain school in a

Mathematics paper consisting of 100 marks are presented in table below. Find the

mean of the marks obtained by the students.

Marks obtained 10 20 36 40 50 56 60 70 72 80 88 92 95

(xi

)

Number of 1 1 3 4 3 2 4 4 1 1 2 31

student ( f

i

)

Solution: Recall that to find the mean marks, we require the product of each xi

with

the corresponding frequency f

i

. So, let us put them in a columnStep-by-step explanation: