Question

The arithmetic mean of the following distribution is 50. Find the missing frequency p
(c.i) 0-20 20-40 40-60 60-80 80-100
(f) 7 6 9 13 p
plz answer this question

Answer 1

Answer:

p=4

Step-by-step explanation:

To answer this question, first we need to build a DISTRIBUTION TABLE with this data.

  (X)             (Xi)             (f)             (Xif)

[0-20)           10               7               70

[20-40)        30              6              180

[40-60)        50              9              450

[60-80)        70              13              910

[80-100)        90              p             90p

*X: Given Intervals

*Xi: Average of the intervals, $Xi=\frac{a+b}{2}$

*f: Number of times X repeats.

*Xif: Sum of each Xi, $Xif=Xi*f$

Having our Distribution Table ready, we can analyze the mean.

The mean is the average of the data we collected.

mean= ∑$\frac{Xi*f}{n}; n$ being the total number of data.

To find p, we have the mean of the data which is 50.

The number of elements is the sum of its frequencies:

$n=7+6+9+13+p$

$n=35+p$

The sum of the Xif column is:

$70+180+450+910+90p= 1610+90p$

Now we can build our equation:

$mean=\frac{1610+90p}{35+p}=50\\  1610+90p=50(35+p)\\ 1610+90p=1750+50p\\ 90p-50p=1750-1610\\ 40p=140\\ p=\frac{140}{40}=3,5$≈4

We have to aproximate to its next integer because a frequency has to be a whole number.

Answer 2

Answer:

mark me brain list

Step-by-step explanation:

Answer:

p=4

Step-by-step explanation:

To answer this question, first we need to build a DISTRIBUTION TABLE with this data.

(X) (Xi) (f) (Xif)

[0-20) 10 7 70

[20-40) 30 6 180

[40-60) 50 9 450

[60-80) 70 13 910

[80-100) 90 p 90p

*X: Given Intervals

*Xi: Average of the intervals, Xi=\frac{a+b}{2}Xi=

2

a+b

*f: Number of times X repeats.

*Xif: Sum of each Xi, Xif=Xi*fXif=Xi∗f

Having our Distribution Table ready, we can analyze the mean.

The mean is the average of the data we collected.

mean= ∑\frac{Xi*f}{n}; n

n

Xi∗f

;n being the total number of data.

To find p, we have the mean of the data which is 50.

The number of elements is the sum of its frequencies:

n=7+6+9+13+pn=7+6+9+13+p

n=35+pn=35+p

The sum of the Xif column is:

70+180+450+910+90p= 1610+90p70+180+450+910+90p=1610+90p

Now we can build our equation:

\begin{gathered}mean=\frac{1610+90p}{35+p}=50\\ 1610+90p=50(35+p)\\ 1610+90p=1750+50p\\ 90p-50p=1750-1610\\ 40p=140\\ p=\frac{140}{40}=3,5\end{gathered}

mean=

35+p

1610+90p

=50

1610+90p=50(35+p)

1610+90p=1750+50p

90p−50p=1750−1610

40p=140

p=

40

140

=3,5

≈4

We have to aproximate to its next integer because a frequency has to be a whole number.