Chapter 1.2, Problem 50E

a.

To determine

To identify if the number of students greater than or less than 20

Answer to Problem 50E

Greater than 20

Explanation of Solution

Given:

  

Concept used:

Mean is the sum of all the data present divided by the given frequency.

Calculation:

In the given figure the following data can be considered:

  

The number of students who attended the:

1^st meeting = 18

2^nd meeting = 21

3^rd meeting = 17

4^th meeting = x (Say)

Also, mean of the four meetings is 20.

Therefore, according to the given condition,

  $\begin{array}{l}\Rightarrow \text{Mean}=\frac{18+21+17+x}{4}\\ \Rightarrow 20=\frac{x+56}{4}\\ \Rightarrow x+56=80\\ \Rightarrow x=24\end{array}$

Conclusion:

Hence, the number of students who attended in the 4^th meeting will be greater than 20.

b.

To determine

To identify the number of students who attended the 4^th meeting.

Answer to Problem 50E

24

Explanation of Solution

Given:

  

Concept used:

Mean is the sum of all the data present divided by the given frequency.

Calculation:

In the given figure the following data can be considered:

  

The number of students who attended the:

1^st meeting = 18

2^nd meeting = 21

3^rd meeting = 17

4^th meeting = x (Say)

Also, mean of the four meetings is 20.

Therefore, according to the given condition,

  $\begin{array}{l}\Rightarrow \text{Mean}=\frac{18+21+17+x}{4}\\ \Rightarrow 20=\frac{x+56}{4}\\ \Rightarrow x+56=80\\ \Rightarrow x=24\end{array}$

Conclusion:

Hence, the number of students who attended in the 4^th meeting will be 24.

c.

To determine

To describe a way to estimate the value in part (b)

Explanation of Solution

Given:

  

Calculation:

From the given graph it is clear that: (negative sign represents less than mean and positive sign represents greater than mean)

Number of students in 1^st meeting with respect to the mean = (18 - 20) = -2

Number of students in 2^nd meeting with respect to the mean = (21 - 20) = +1

Number of students in 3^rd meeting with respect to the mean = (17 - 20) = -3

Now, the mean has to be 20 after considering the count of 4^th meeting.

The net coming out of the previous 3 meetings should be added to 20 to attain the number of students required for the 4^th meeting.

Therefore, Net = (-2) + 1 + (-3) = -4, which means the net value is short of 4 units which should be added to the mean to obtain the 4^th value.

Hence, the number of students in the 4^th meeting will be = 20 + 4 = 24.

Conclusion:

Hence, by the above method the data could be manipulated to obtain the required data.