Chapter 11.6, Problem 26PPSE

Solution

a.

Tocalculate:The value of f in the table. If mean of the exam scores is 3.5

Score	1	2	3	4	5
Frequency	1	3	f	12	3

The value of f is 7.

Given information:

The given table is:

Score	1	2	3	4	5
Frequency	1	3	f	12	3

Formula used:

  $Mean=\frac{\sum xf}{\sum f}$

Calculation:

Consider the given table.

Score	1	2	3	4	5
Frequency	1	3	f	12	3	$\sum f=19+f$
xf	1	6	3f	48	15	$\sum xf=70+3f$

It is given mean of the exam scores is 3.5

  $\begin{array}{c}Mean=\frac{70+3f}{19+f}\\ 3.5\left(19+f\right)=70+3f\\ 66.5+3.5f=70+3f\\ 0.5f=3.5\\ f=7\end{array}$

The value of f is 7.

b.

To identify:The mode of all the exam scores.

Score	1	2	3	4	5
Frequency	1	3	f	12	3

The mode of the data is 4.

Given information:

The given table is:

Score	1	2	3	4	5
Frequency	1	3	f	12	3

Explanation:

Consider the given information.

Mode of the data is the data value with highest frequency.

It can be observed that 4 has the highest frequency that is 12.

Thus, the mode of the data is 4.

c.

To identify:The median of all the exam scores.

Score	1	2	3	4	5
Frequency	1	3	f	12	3

The median of the data is 4.

Given information:

The given table is:

Score	1	2	3	4	5
Frequency	1	3	f	12	3

Explanation:

Consider the given information.

The total number of data values is $\sum f=19+7=26$

Median is the middle value of the ordered data set. So median of the given data set will be the average of 13^th and 14^th data values. Data values at 13^th and 14^th position are both 4.

So, median of the data set is 4.